Question 1

The diagonals of a rhombus are 24 cm and 10 cm. What is the perimeter of the rhombus?

Accepted Answer

Step 1: In a rhombus, diagonals bisect each other at right angles. So half-diagonals are 12 cm and 5 cm. Step 2: Each side of the rhombus = √(12² + 5²) = √(144 + 25) = √169 = 13 cm. Step 3: Perimeter = 4 × 13 = 52 cm. Therefore, answer is 52 cm.

Question 2

The diagonals of a rhombus are 16 cm and 12 cm. Find its area.

Accepted Answer

Step 1: Use area formula for rhombus: Area = (d₁ × d₂) / 2, where d₁ and d₂ are diagonals. Step 2: Area = (16 × 12) / 2 = 192 / 2 = 96 cm².

Question 3

The area of a square is 256 cm². What is the length of its side?

Accepted Answer

Step 1: Recall that area of a square = side². Step 2: If side² = 256, then side = √256. Step 3: side = 16 cm. Therefore, the length of the side is 16 cm.

Question 4

The perimeter of a rectangle is 56 cm. If the length is 18 cm, what is the area of the rectangle?

Accepted Answer

Step 1: Use perimeter formula for rectangle: P = 2(l + b). Step 2: Substitute: 56 = 2(18 + b). Step 3: 28 = 18 + b, so b = 10 cm. Step 4: Area = l × b = 18 × 10 = 180 cm².

Question 5

A parallelogram has a base of 24 cm and height of 15 cm. What is its area?

Accepted Answer

Step 1: Use area formula for parallelogram: Area = base × height. Step 2: Area = 24 × 15 = 360 cm².

Question 6

The perimeter of a rectangle is 56 cm. If its length is 18 cm, what is its breadth?

Accepted Answer

Step 1: Recall the formula for perimeter of a rectangle: P = 2(l + b). Step 2: Substitute P = 56 cm and l = 18 cm. Step 3: 56 = 2(18 + b). Step 4: 28 = 18 + b. Step 5: b = 28 - 18 = 10 cm. Therefore, the breadth is 10 cm.

Question 7

A trapezium has parallel sides of 10 cm and 14 cm, and height 8 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for area of a trapezium: Area = (sum of parallel sides / 2) × height. Step 2: Substitute the parallel sides as 10 cm and 14 cm, and height as 8 cm. Step 3: Area = ((10 + 14) / 2) × 8 = (24 / 2) × 8 = 12 × 8 = 96 cm². Therefore, the area is 96 cm².

Question 8

A rhombus has diagonals of length 16 cm and 12 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for area of a rhombus: Area = (d₁ × d₂) / 2, where d₁ and d₂ are the diagonals. Step 2: Substitute d₁ = 16 cm and d₂ = 12 cm. Step 3: Area = (16 × 12) / 2 = 192 / 2 = 96 cm². Therefore, the area is 96 cm².

Question 9

A rectangle has length 24 cm and breadth 18 cm. What is the perimeter of the rectangle?

Accepted Answer

Step 1: Identify the formula for perimeter of a rectangle: P = 2(l + b). Step 2: Substitute l = 24 cm and b = 18 cm. Step 3: P = 2(24 + 18) = 2(42) = 84 cm. Therefore, the perimeter is 84 cm.

Question 10

A parallelogram has base 20 cm and height 15 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for area of a parallelogram: Area = base × height. Step 2: Substitute base = 20 cm and height = 15 cm. Step 3: Area = 20 × 15 = 300 cm². Therefore, the area is 300 cm².

Question 11

A parallelogram has adjacent sides of length 12 cm and 8 cm. If the angle between them is 60°, what is the area of the parallelogram?

Accepted Answer

Step 1: For a parallelogram, Area = base × height = a × b × sin(θ), where a and b are adjacent sides and θ is the included angle. Step 2: Area = 12 × 8 × sin(60°) = 12 × 8 × (√3/2) = 96 × (√3/2) = 48√3 ≈ 48 × 1.732 = 83.14 cm². Step 3: Rounding to nearest clean value: 48√3 cm² or approximately 83.14 cm². For SSC purposes, the exact answer is 48√3 cm².

Question 12

A parallelogram has adjacent sides of length 12 cm and 8 cm. If the angle between these sides is 60°, what is the area of the parallelogram?

Accepted Answer

Step 1: The area of a parallelogram is given by the formula: Area = base × height, or equivalently Area = a × b × sin(θ), where a and b are adjacent sides and θ is the included angle. Step 2: Here, a = 12 cm, b = 8 cm, and θ = 60°. Step 3: Area = 12 × 8 × sin(60°) = 96 × (√3/2) = 48√3 cm². Step 4: 48√3 ≈ 48 × 1.732 = 83.14 cm². However, the exact answer is 48√3 cm², which equals approximately 83.1 cm² or can be expressed as 48√3.

Question 13

A rhombus has diagonals of length 16 cm and 12 cm. What is the perimeter of the rhombus?

Accepted Answer

Step 1: In a rhombus, the diagonals bisect each other at right angles. Step 2: Half-diagonals are 8 cm and 6 cm. Step 3: Using Pythagoras theorem, side of rhombus = √(8² + 6²) = √(64 + 36) = √100 = 10 cm. Step 4: Perimeter = 4 × side = 4 × 10 = 40 cm.

Question 14

In a rectangle PQRS, the length is 20 cm and the width is 15 cm. A diagonal is drawn from P to R. What is the ratio of the area of triangle PQR to the area of the rectangle PQRS?

Accepted Answer

Step 1: The area of rectangle PQRS = length × width = 20 × 15 = 300 cm². Step 2: When a diagonal is drawn in a rectangle, it divides the rectangle into two congruent triangles. Step 3: The area of triangle PQR = (1/2) × area of rectangle = (1/2) × 300 = 150 cm². Step 4: The ratio of area of triangle PQR to area of rectangle = 150 : 300 = 1 : 2.

Question 15

A square has a side length of 10 cm. If a diagonal of the square is drawn, what is the ratio of the diagonal to the side of the square?

Accepted Answer

Step 1: For a square with side a, the diagonal d = a√2 (from Pythagoras theorem: d = √(a² + a²) = √(2a²) = a√2). Step 2: With side = 10 cm, diagonal = 10√2 cm. Step 3: Ratio of diagonal to side = (10√2)/10 = √2 ≈ 1.414 or simply √2:1.

Question 16

In a quadrilateral ABCD, the diagonals AC and BD intersect at point O. If AC = 20 cm, BD = 16 cm, and the diagonals are perpendicular to each other, what is the area of the quadrilateral?

Accepted Answer

Step 1: When diagonals of a quadrilateral are perpendicular, the area formula is: Area = (1/2) × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals. Step 2: Area = (1/2) × 20 × 16 = (1/2) × 320 = 160 cm².

Question 17

A rectangle has length 15 cm and breadth 8 cm. A diagonal is drawn. What is the length of the diagonal?

Accepted Answer

Step 1: In a rectangle, the diagonal forms a right triangle with length and breadth as the two sides. Step 2: Using Pythagoras theorem: diagonal = √(length² + breadth²) = √(15² + 8²) = √(225 + 64) = √289 = 17 cm.

Question 18

In trapezoid PQRS, PQ is parallel to RS. The non-parallel sides PS and QR are equal in length (isosceles trapezoid). If PQ = 28 cm, RS = 16 cm, and the height of the trapezoid is 12 cm, find the length of the equal sides PS and QR.

Accepted Answer

Step 1: In an isosceles trapezoid, drop perpendiculars from R and S to line PQ, meeting at points M and N respectively. Step 2: Since the trapezoid is isosceles, PM = QN = (PQ - RS)/2 = (28 - 16)/2 = 6 cm. Step 3: Now, in right triangle PSM (or QRN), we have SM = 12 cm (height) and PM = 6 cm. Step 4: Using Pythagoras theorem: PS² = PM² + SM² = 6² + 12² = 36 + 144 = 180. Step 5: PS = √180 = 6√5 cm ≈ 13.42 cm. Therefore, the answer is 6√5 cm.

SSC CHSL Quadrilaterals

SSC CHSL Quadrilaterals — Past Exam Questions

Quadrilaterals— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Quadrilaterals — Practice Questions

60-Second Revision — Quadrilaterals