Quantitative Aptitude PYQs

Shortcut Trick

Profit = Selling Price − Cost Price = 440 − 400 = 40.

Profit % = (Profit ÷ CP) × 100 = (40 ÷ 400) × 100.

Profit % = 1/10 × 100 = 10%.

∴ The correct answer is 10%.

Alternate Method

Given:

Cost Price (CP) of the calculator = ₹400

Selling Price (SP) of the calculator = ₹440

Formula Used:

Profit = Selling Price − Cost Price

Profit Percentage (%) = (Profit ÷ Cost Price) × 100

Calculations:

⇒ Profit = 440 − 400 = ₹40

⇒ Profit Percentage = (40 ÷ 400) × 100

⇒ Profit Percentage = (1 ÷ 10) × 100

⇒ Profit Percentage = 10%

∴ The correct answer is 10%.

Additional Information

Loss Percentage

When CP > SP, a loss occurs. Loss % = [(CP − SP) ÷ CP] × 100.

Selling Price Formula

To find SP when profit % is given: SP = CP × [(100 + Profit %) ÷ 100].

Cost Price Formula

To find CP when SP and profit % are given: CP = [SP × 100] ÷ (100 + Profit %).

Shortcut Trick

Net result of Markup percentage and Discount percentage is given by the formula: Profit% = a + b + (ab/100).

Here, a (Markup) = +40 and b (Discount) = −20.

Profit percentage = 40 − 20 − (40 × 20 / 100)

Profit percentage = 20 − 8 = 12%.

∴ The correct answer is 12%.

Alternate Method

Given:

Markup percentage = 40% above Cost Price (CP)

Discount percentage = 20% on Marked Price (MP)

Calculations:

⇒ Let the Cost Price (CP) of the goods be ₹100.

⇒ Marked Price (MP) = CP + 40% of CP = 100 + 40 = ₹140.

⇒ Discount = 20% of MP = 0.20 × 140 = ₹28.

⇒ Selling Price (SP) = MP − Discount = 140 − 28 = ₹112.

⇒ Profit = SP − CP = 112 − 100 = ₹12.

⇒ Profit percentage = (Profit / CP) × 100 = (12 / 100) × 100 = 12%.

∴ The correct answer is 12%.

Additional Information

Marked Price (MP)

It is the price set by the seller above the Cost Price to allow for discounts while still maintaining a profit margin.

Discount and Selling Price

Discount is always calculated on the Marked Price. The formula is: Selling Price = Marked Price − Discount.

Relation between CP, MP, and Profit

The relationship can be expressed as: MP / CP = (100 + Profit%) / (100 − Discount%).

Successive Percentage Change

When a value is changed by x% and then by y%, the net effective change is [x + y + (xy/100)]%.

Shortcut Trick

Ratio of Salaries of A and B = 4 : 5

Value for A = 4 units → ₹40

Multiplier = 40 ÷ 4 = 10

Value for B = 5 units × 10 = ₹50

∴ The correct answer is ₹50.

Alternate Method

Given:

Ratio of salaries (A : B) = 4 : 5

Salary of A = ₹40

Calculations:

⇒ Let the salaries of A and B be 4x and 5x respectively.

⇒ Salary of A = 4x = 40

⇒ x = 40 ÷ 4

⇒ x = 10

⇒ Salary of B = 5x

⇒ Salary of B = 5 × 10

⇒ Salary of B = ₹50

Therefore, Option (4) is the correct choice.

∴ The correct answer is ₹50.

Additional Information

Concept of Ratio

A ratio is a comparison of two quantities of the same kind. If two quantities are in the ratio a:b, they can be represented as ax and bx, where x is the common multiplier.

Unitary Method in Ratios

In the unitary method, we find the value of a single unit (x) by dividing the given value by its corresponding ratio part, then multiply by the required ratio part.

Proportionality

If A/B = 4/5, then B = (5/4) × A. This linear relationship ensures that any change in one quantity reflects proportionally in the other.

Shortcut Trick

Simple Interest (SI) for 1 year = Total Interest ÷ Time

SI for 1 year = 432 ÷ 3 = ₹144

Rate of Interest = (SI for 1 year ÷ Principal) × 100

Rate % = (144 ÷ 1200) × 100 = 12%

∴ The correct answer is 12%.

Alternate Method

Given:

Principal (P) = ₹1200

Simple Interest (SI) = ₹432

Time (T) = 3 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ 432 = (1200 × R × 3) ÷ 100

⇒ 432 = 12 × R × 3

⇒ 432 = 36 × R

⇒ R = 432 ÷ 36

⇒ R = 12%

∴ The correct answer is 12%.

Additional Information

Simple Interest Definition

Simple Interest is calculated only on the principal amount of a loan or deposit. It does not earn interest on interest.

Total Amount Formula

The total Amount (A) to be paid back after T years is A = P + SI, which can be written as A = P(1 + RT/100).

Variable Units

Always ensure that the Rate (R) and Time (T) are in the same time units (e.g., both per annum and years) before calculation.

Shortcut Trick

Speed in m/s = Distance ÷ Time = 100 ÷ 10 = 10 m/s

Convert m/s to km/h by multiplying with 18/5.

Speed = 10 × (18 ÷ 5) = 2 × 18 = 36 km/h.

∴ The correct answer is 36 km/h.

Alternate Method

Given:

Length of the train (Distance) = 100 m

Time taken to pass the pole = 10 sec

Formula Used:

Speed = Distance ÷ Time

To convert speed from m/s to km/h, multiply by 18/5.

Calculations:

⇒ Speed = 100 ÷ 10

⇒ Speed = 10 m/s

⇒ Speed in km/h = 10 × (18 ÷ 5)

⇒ Speed = 2 × 18

⇒ Speed = 36 km/h

∴ The correct answer is 36 km/h.

Additional Information

Unit Conversion Rules

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Crossing Different Objects

When a train crosses a point object (pole, man), distance = length of train. When it crosses a platform or bridge, distance = length of train + length of platform.

Relative Speed

If two objects move in the same direction at speeds u and v, relative speed = |u − v|. If they move in opposite directions, relative speed = u + v.

Shortcut Trick

Since the Distance is constant, Speed is inversely proportional to Time.

Ratio of Speeds (S₁ : S₂) = 48 : 60 = 4 : 5.

Ratio of Times (T₁ : T₂) = 5 : 4.

Given 5 units = 50 min ⇒ 1 unit = 10 min.

Required Time (4 units) = 4 × 10 = 40 min.

∴ The correct answer is 40 min.

Alternate Method

Given:

Initial Speed (S₁) = 48 km/h

Initial Time (T₁) = 50 min = 50 ÷ 60 hours

New Speed (S₂) = 60 km/h

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Distance = S₁ × T₁

⇒ Distance = 48 × (50 ÷ 60) km

⇒ Distance = 48 × (5 ÷ 6) = 8 × 5 = 40 km

⇒ New Time (T₂) = Distance ÷ S₂

⇒ T₂ = 40 ÷ 60 hours

⇒ T₂ in minutes = (40 ÷ 60) × 60 min

⇒ T₂ = 40 min

∴ The correct answer is 40 min.

Additional Information

Relationship between Speed and Time

When Distance is constant, Speed and Time are inversely proportional: S₁ × T₁ = S₂ × T₂.

Unit Conversion

To convert km/h to m/s, multiply by 5 ÷ 18. To convert m/s to km/h, multiply by 18 ÷ 5.

Average Speed

If a certain distance is covered at speed 'a' and the same distance is covered at speed 'b', the Average Speed = 2ab ÷ (a + b).

Shortcut Trick

In recasting problems, the total volume remains constant.

Volume of n small cones = Volume of 1 large cone

n × (1/3 × π × r² × h) = 1/3 × π × R² × H

Cancel 1/3 and π from both sides: 5 × 3² × 4 = R² × 10

⇒ 180 = 10 × R² ⇒ R² = 18 ⇒ R = √18 ≈ 4.24 cm.

∴ The correct answer is 4.24 cm.

Alternate Method

Given:

Number of small cones (n) = 5

Radius of small cone (r) = 3 cm

Height of small cone (h) = 4 cm

Height of new cone (H) = 10 cm

Formula Used:

Volume of a right circular cone = (1/3) × π × r² × h

Calculations:

⇒ Total Volume of 5 small cones = 5 × [(1/3) × 3.14 × (3)² × 4]

⇒ Total Volume = 5 × (1/3) × 3.14 × 9 × 4 = 15 × 3.14 × 4 = 188.4 cm³

⇒ Volume of the single recast cone = (1/3) × 3.14 × R² × 10

⇒ Since volumes are equal: 188.4 = (31.4 / 3) × R²

⇒ R² = (188.4 × 3) / 31.4

⇒ R² = 6 × 3 = 18

⇒ R = √18 = √(9 × 2) = 3√2

⇒ R = 3 × 1.414 = 4.242 cm

∴ The correct answer is 4.24 cm.

Additional Information

Volume Conservation

When a solid is melted and recast into another shape, the Total Volume remains identical, although surface area may change.

Slant Height of a Cone

The slant height (l) is the distance from the apex to the edge of the base: l = √(r² + h²).

Surface Area Formulas

Curved Surface Area (CSA) = πrl and Total Surface Area (TSA) = πr(l + r).

Recasting into different shapes

If recast into a sphere, equate volume to (4/3)πR³; if a cylinder, equate to πR²H.

Shortcut Trick

The capacity of a cuboidal pond is the product of its three dimensions: Length × Breadth × Depth.

Capacity = 25 × 18 × 4

Shortcut Calculation: (25 × 4) × 18 = 100 × 18 = 1800 m³

∴ The correct answer is 1800 m³.

Alternate Method

Given:

Length (l) = 25 m

Breadth (b) = 18 m

Depth (h) = 4 m

Formula Used:

Capacity (Volume) of a Cuboid = l × b × h

Calculations:

⇒ Volume = 25 × 18 × 4

⇒ Volume = 450 × 4

⇒ Volume = 1800 m³

∴ The correct answer is 1800 m³.

Additional Information

Volume of a Cube

If all dimensions are equal (side = a), the volume is given by a³.

Total Surface Area of a Cuboid

The total area of all six faces is 2 × (lb + bh + hl).

Capacity Conversion

To convert cubic meters to liters, multiply by 1000 (1 m³ = 1000 liters).

Diagonal of a Cuboid

The length of the longest rod that can fit is √(l² + b² + h²).

Shortcut Trick

Identify the base as a Right-Angled Triangle because 7, 24, and 25 form a Pythagorean triplet (7² + 24² = 25²).

Base Area = (1/2) × Product of legs = (1/2) × 7 × 24 = 84 cm².

Volume of Prism = Base Area × Height = 84 × 15 = 1260 cm³.

∴ The correct answer is 1260 cm³.

Alternate Method

Given:

Sides of the triangular base: a = 7 cm, b = 24 cm, c = 25 cm.

Height of the prism (h) = 15 cm.

Formula Used:

Volume of Prism = Area of Base × Height

Area of Triangle (if sides form a right angle) = (1/2) × base × perpendicular

Calculations:

⇒ First, verify if the base is a right-angled triangle: 7² + 24² = 49 + 576 = 625.

⇒ Since 25² = 625, the base is a right-angled triangle.

⇒ Area of the base = (1/2) × 7 × 24

⇒ Area of the base = 7 × 12 = 84 cm².

⇒ Volume of the prism = 84 × 15

⇒ Volume of the prism = 1260 cm³.

Thus, the calculated volume corresponds to Option (2).

∴ The correct answer is 1260 cm³.

Additional Information

Volume of a Right Prism

The volume is always the product of the Base Area and the Vertical Height (V = A × h).

Surface Area of Prism

Lateral Surface Area = Perimeter of base × Height. Total Surface Area = LSA + 2 × Base Area.

Heron's Formula

For non-right triangles, Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.

Common Pythagorean Triplets

Useful sets include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Shortcut Trick

Third side of triangular base = √(7² + 9²) = √130 = 11.4 cm

Perimeter of base = 7 + 9 + 11.4 = 27.4 cm

Height of prism = Lateral Surface Area ÷ Perimeter

Height = 360 ÷ 27.4 ≈ 13.14 cm

∴ The correct answer is 13.14 cm.

Alternate Method

Given:

Lateral Surface Area (LSA) = 360 cm²

Smaller sides of the triangular base (a, b) = 7 cm, 9 cm

Value of √130 = 11.4 cm

Formula Used:

Lateral Surface Area (LSA) = Perimeter of base × Height (h)

Hypotenuse of base (c) = √(a² + b²)

Calculations:

⇒ Third side of base (c) = √(7² + 9²)

⇒ c = √(49 + 81) = √130

⇒ c = 11.4 cm

⇒ Perimeter (P) = 7 + 9 + 11.4 = 27.4 cm

⇒ 360 = 27.4 × h

⇒ h = 360 ÷ 27.4

⇒ h = 13.1386...

⇒ h ≈ 13.14 cm

∴ The correct answer is 13.14 cm.

Additional Information

Total Surface Area (TSA) of Prism

TSA = Lateral Surface Area + 2 × (Area of the Base). For a right triangular base, Area = 1/2 × base × height.

Volume of a Prism

Volume = Area of the Base × Height of the prism. Units are expressed in cubic centimeters (cm³).

Right Prism Definition

A right prism is a prism in which the joining edges and faces are perpendicular to the base faces.

Shortcut Trick

Wage of leaving worker = Old Average + (Remaining Workers × Decrease in Average)

Wage = 250 + (7 × (250 − 240))

Wage = 250 + (7 × 10) = ₹320

∴ The correct answer is ₹320.

Alternate Method

Given: Average daily wage of 8 workers = ₹250. Average daily wage of 7 workers = ₹240.

Formula Used: Total Sum = Average × Number of observations

⇒ Total wage of 8 workers = 8 × 250 = ₹2000 ⇒ Total wage of 7 workers (remaining) = 7 × 240 = ₹1680 ⇒ Wage of worker who left = Total wage of 8 workers − Total wage of 7 workers ⇒ Wage = 2000 − 1680 ⇒ Wage = ₹320

∴ The correct answer is ₹320.

Additional Information

Average Definition

Average is the sum of all observations divided by the total number of observations. (Average = Sum ÷ n)

Exclusion Rule

If the average decreases when a person leaves, it means the person's value was greater than the initial average. If the average increases, the person's value was lower than the initial average.

Sum Formula

To find the total amount when average and count are known: Sum = Average × Count.

Shortcut Trick

Remaining value after 20% discount = 80% of 500 = ₹400.

Further reduction of ₹20 from the balance = 400 − 20 = ₹380.

∴ The correct answer is ₹380.

Alternate Method

Given:

Marked Price (MP) = ₹500

First Discount = 20%

Second Reduction = ₹20

Formula Used:

Price after % discount = MP × (100 − Discount%)/100

Final Selling Price = Price after % discount − Flat Reduction

Calculations:

⇒ Discount amount = 20% of 500 = (20/100) × 500 = ₹100

⇒ Price after first discount = 500 − 100 = ₹400

⇒ Final Selling Price = 400 − 20 = ₹380

∴ The correct answer is ₹380.

Additional Information

Successive Discounts

When two successive discounts d₁% and d₂% are given, the single equivalent discount is (d₁ + d₂ − (d₁ × d₂)/100)%.

Marked Price (MP)

The price printed on the label of an article is called the Marked Price or List Price. Discounts are always calculated on the MP.

Selling Price (SP) Formula

SP = MP − Discount. If profit occurs, SP = Cost Price (CP) + Profit; if loss occurs, SP = CP − Loss.

Shortcut Trick

The radius of a circle is calculated by dividing the circumference by 2π.

Given Circumference = 31.4 cm and π = 3.14.

Radius (r) = 31.4 ÷ (2 × 3.14)

r = 31.4 ÷ 6.28 = 5 cm.

∴ The correct answer is 5 cm.

Alternate Method

Given:

Circumference of the circle (C) = 31.4 cm

Value of Pi (π) = 3.14

Formula Used:

Circumference of a circle = 2πr

Where 'r' is the radius of the circle.

Calculations:

⇒ 31.4 = 2 × 3.14 × r

⇒ 31.4 = 6.28 × r

⇒ r = 31.4 ÷ 6.28

⇒ r = 5 cm

∴ The correct answer is 5 cm.

Additional Information

Area of a Circle

The total space enclosed within the boundary of a circle is given by Area = πr².

Diameter of a Circle

The diameter is the longest chord of a circle and is exactly twice the radius (d = 2r).

Perimeter of a Semicircle

The boundary length of a half-circle including the diameter is calculated as (πr + 2r).

Shortcut Trick

Convert the failure marks into a percentage of the total marks.

Failure % = (50 ÷ 500) × 100 = 10%.

Passing % = Scored % + Failure %.

Passing % = 30% + 10% = 40%.

∴ The correct answer is 40%.

Alternate Method

Given:

Total Marks = 500

Scored Percentage = 30%

Failing Marks = 50

Formula Used:

Passing Marks = Marks Obtained + Failing Marks

Passing Percentage = (Passing Marks ÷ Total Marks) × 100

Calculations:

⇒ Marks Scored = 30% of 500

⇒ Marks Scored = (30 ÷ 100) × 500 = 150

⇒ Required Passing Marks = 150 + 50 = 200

⇒ Passing Percentage = (200 ÷ 500) × 100

⇒ Passing Percentage = (2 ÷ 5) × 100 = 40%

∴ The correct answer is 40%.

Additional Information

Passing Criteria

Passing Marks = Marks Obtained + Failing Marks. If a student passes by extra marks, then Passing Marks = Marks Obtained − Extra Marks.

Percentage Calculation

To find what percentage X is of Y, use the formula: (X ÷ Y) × 100. In this case, (Passing Marks ÷ Total Marks) × 100.

Total Marks Formula

If the difference in percentages and the difference in marks are known, Total Marks = (Difference in Marks × 100) ÷ Difference in Percentages.

Shortcut Trick

At a 20% loss, the Selling Price (SP) is 80% of the Cost Price (CP).

SP = 80% × 400

SP = 0.8 × 400 = 320

∴ The correct answer is ₹320.

Alternate Method

Given: Cost Price (CP) = ₹400, Loss Percentage = 20%

Formula Used: Selling Price (SP) = CP − (Loss% × CP / 100)

⇒ Cost Price (CP) = ₹400

⇒ Loss Percentage = 20%

⇒ Loss Amount = (20/100) × 400 = ₹80

⇒ Selling Price (SP) = CP − Loss

⇒ SP = 400 − 80 = 320

∴ The correct answer is ₹320.

Additional Information

Profit and Loss Percentage

Profit = SP − CP and Loss = CP − SP. Both percentages are always calculated on the Cost Price (CP) unless stated otherwise.

Direct Calculation of Selling Price

For profit, SP = CP × (100 + P%)/100. For loss, SP = CP × (100 − L%)/100.

Marked Price and Discount

Discount is always allowed on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Total ratio parts = 2 + 7 = 9 units

Total savings given = ₹180

9 units = ₹180 → 1 unit = ₹20

A's savings (2 units) = 2 × 20 = ₹40

∴ The correct answer is ₹40.

Alternate Method

Given:

Ratio of monthly savings of A and B = 2 : 7

Total savings of A and B = ₹180

Let the monthly savings of A and B be 2x and 7x respectively.

⇒ Total savings = 2x + 7x = 180

⇒ 9x = 180

⇒ x = 180 ÷ 9

⇒ x = 20

⇒ A's savings = 2x = 2 × 20 = 40

∴ The correct answer is ₹40.

Additional Information

Ratio Division Rule

To divide a quantity 'S' in the ratio a:b, the first part is (a / (a+b)) × S and the second part is (b / (a+b)) × S.

Compound Ratio

The compound ratio of a:b and c:d is calculated as (a × c) : (b × d).

Inverse Ratio

The inverse ratio of a:b is b:a, which is obtained by swapping the antecedent and the consequent.

Shortcut Trick

Total Interest Percentage = Rate × Time = 8% × 4 = 32%

Given that 32% of Principal = ₹184

1% of Principal = 184 ÷ 32 = 5.75

100% (Principal) = 5.75 × 100 = ₹575

∴ The correct answer is ₹575.

Alternate Method

Given:

Simple Interest (SI) = ₹184

Rate (R) = 8% p.a.

Time (T) = 4 years

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 184 = (P × 8 × 4) ÷ 100

⇒ 184 = (P × 32) ÷ 100

⇒ 184 × 100 = 32P

⇒ 18400 = 32P

⇒ P = 18400 ÷ 32

⇒ P = 575

∴ The correct answer is ₹575.

Additional Information

Total Amount Formula

The total amount (A) is the sum of the principal and interest: A = P + SI = P(1 + (R × T) ÷ 100).

Finding the Rate of Interest

To calculate the annual rate when other variables are known: R = (SI × 100) ÷ (P × T).

Difference between SI and CI

Simple Interest remains constant every year because it is only calculated on the Principal, unlike Compound Interest which includes interest on interest.

Shortcut Trick

Downstream Speed = 24 ÷ 2 = 12 km/h

Upstream Speed = 8 ÷ 2 = 4 km/h

Stream Speed = (Downstream − Upstream) ÷ 2

Stream Speed = (12 − 4) ÷ 2 = 4 km/h

∴ The correct answer is 4 km/h.

Alternate Method

Given:

Downstream Distance = 24 km, Time = 2 hours

Upstream Distance = 8 km, Time = 2 hours

Formula Used:

Speed = Distance ÷ Time

Speed of Stream (y) = (u − v) ÷ 2, where u = Downstream speed and v = Upstream speed.

⇒ Downstream Speed (u) = 24 ÷ 2 = 12 km/h

⇒ Upstream Speed (v) = 8 ÷ 2 = 4 km/h

⇒ Let the Speed of Boat in Still Water be x and Speed of Stream be y.

⇒ x + y = 12

⇒ x − y = 4

⇒ Subtracting the equations: (x + y) − (x − y) = 12 − 4

⇒ 2y = 8

⇒ y = 4 km/h

∴ The correct answer is 4 km/h.

Additional Information

Speed of Boat in Still Water

It is the average of downstream and upstream speeds: x = (u + v) ÷ 2.

Relative Speed Concept

Downstream speed is always greater than upstream speed because the Stream aids the motion.

Speed Ratios

If the time taken to travel the same distance downstream and upstream is t₁ and t₂, then (x/y) = (t₂ + t₁) ÷ (t₂ − t₁).

Shortcut Trick

Ratio of Sides (Initial : New) = 1 : 2

Ratio of Areas = (Initial Side)² : (New Side)²

Ratio of Areas = 1² : 2² = 1 : 4

New Area is 4 times the initial area, which represents 400% of the original value.

∴ The correct answer is 400%.

Alternate Method

Given:

Initial side of the square = s

New side of the square = 2s (doubled)

Formula Used:

Area of square = (side)²

Percentage = (New Value / Original Value) × 100

Calculations:

⇒ Initial Area (A₁) = s²

⇒ New Area (A₂) = (2s)² = 4s²

⇒ Area calculation in percentage = (A₂ / A₁) × 100

⇒ (4s² / s²) × 100

⇒ 4 × 100 = 400%

∴ The correct answer is 400%.

Additional Information

Area and Perimeter of a Square

For a square with side 'a', the Area = a² and the Perimeter = 4a.

Scaling Effect on Area

If the linear dimensions of a 2D shape are multiplied by a factor 'k', the Area is multiplied by k².

Successive Percentage Change

The change in area can also be calculated using the successive percentage formula: x + y + (xy/100), where x and y are the percentage changes in the dimensions.

Diagonal of a Square

The length of the Diagonal = a√2. If the side is doubled, the diagonal also doubles.

Shortcut Trick

Total Area = Number of rooftops × (1/2 × Base × Height)

Total Area = 4 × (1/2 × 10 × 6)

Total Area = 4 × 30 = 120

∴ The correct answer is 120 cm².

Alternate Method

Given:

Base of the triangular rooftop (b) = 10 m

Height of the triangular rooftop (h) = 6 m

Number of identical rooftops (n) = 4

Formula Used:

Area of a Triangle = 1/2 × base × height

Calculations:

⇒ Area of one triangular rooftop = 1/2 × 10 × 6

⇒ Area of one triangular rooftop = 5 × 6 = 30 m²

⇒ Total area of 4 such identical rooftops = 4 × 30

⇒ Total area = 120

∴ The correct answer is 120 cm².

Additional Information

Area of Equilateral Triangle

If all sides of the triangular rooftop are equal (side 'a'), Area = (√3/4) × a².

Heron's Formula

For a triangle with sides a, b, and c: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.

Right-Angled Triangle

In a right-angled triangle, the base and height are the two sides forming the 90° angle.