Question 1

A rectangle has length 24 cm and breadth 16 cm. What is the perimeter of the rectangle?

Accepted Answer

Step 1: Recall the formula for perimeter of a rectangle: P = 2(l + b). Step 2: Substitute l = 24 cm and b = 16 cm. Step 3: P = 2(24 + 16) = 2(40) = 80 cm. Therefore, the perimeter is 80 cm.

Question 2

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

Accepted Answer

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

Question 3

A parallelogram has base 18 cm and height 10 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for area of a parallelogram: A = base × height. Step 2: Substitute base = 18 cm and height = 10 cm. Step 3: A = 18 × 10 = 180 cm². Therefore, the area is 180 cm².

Question 4

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

Accepted Answer

Step 1: Recall the formula for area of a trapezium: A = (1/2) × (sum of parallel sides) × height. Step 2: Substitute the parallel sides as 14 cm and 10 cm, and height = 8 cm. Step 3: A = (1/2) × (14 + 10) × 8 = (1/2) × 24 × 8 = (1/2) × 192 = 96 cm². Therefore, the area is 96 cm².

Question 5

A square has side length 15 cm. What is the length of its diagonal?

Accepted Answer

Step 1: Recall that for a square with side length a, the diagonal d = a√2. Step 2: Substitute a = 15 cm. Step 3: d = 15√2 cm. Step 4: Calculate 15√2 ≈ 15 × 1.414 = 21.21 cm. However, the exact answer is 15√2 cm. If numerical form is required: approximately 21.2 cm (or 21 cm if rounding). The standard answer is 15√2 cm.

Question 6

A rectangle has length 20 cm and diagonal 25 cm. What is the breadth of the rectangle?

Accepted Answer

Step 1: Use the Pythagorean theorem for a rectangle: diagonal² = length² + breadth². Step 2: Substitute diagonal = 25 cm and length = 20 cm. Step 3: 25² = 20² + b². Step 4: 625 = 400 + b². Step 5: b² = 625 - 400 = 225. Step 6: b = √225 = 15 cm. Therefore, the breadth is 15 cm.

Question 7

A parallelogram has a base of 24 cm and a height of 15 cm. If the base is increased by 25% and the height is decreased by 20%, what is the percentage change in the area of the parallelogram?

Accepted Answer

Step 1: Original area = base × height = 24 × 15 = 360 cm². Step 2: New base = 24 + (25% of 24) = 24 + 6 = 30 cm. Step 3: New height = 15 − (20% of 15) = 15 − 3 = 12 cm. Step 4: New area = 30 × 12 = 360 cm². Step 5: Percentage change = [(360 − 360) / 360] × 100 = 0%. Therefore, the area remains unchanged.

Question 8

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, diagonals bisect each other at right angles. Step 2: Half of diagonal 1 = 16/2 = 8 cm. Half of diagonal 2 = 12/2 = 6 cm. Step 3: These half-diagonals form a right triangle with the side of the rhombus as the hypotenuse. Step 4: Using Pythagoras theorem: side = √(8² + 6²) = √(64 + 36) = √100 = 10 cm. Step 5: Perimeter = 4 × side = 4 × 10 = 40 cm.

Question 9

A trapezium has parallel sides of 18 cm and 12 cm, and the perpendicular distance between them is 8 cm. What is its area?

Accepted Answer

Step 1: Area of trapezium = (1/2) × (sum of parallel sides) × height. Step 2: Area = (1/2) × (18 + 12) × 8. Step 3: Area = (1/2) × 30 × 8. Step 4: Area = 15 × 8 = 120 cm². Therefore, the area is 120 cm².

Question 10

In a rectangle, the length is 3 cm more than the width. If the perimeter is 54 cm, what is the area of the rectangle?

Accepted Answer

Step 1: Let width = w cm. Then length = (w + 3) cm. Step 2: Perimeter = 2(length + width) = 2(w + 3 + w) = 2(2w + 3) = 4w + 6. Step 3: Given perimeter = 54 cm, so 4w + 6 = 54. Step 4: 4w = 48, therefore w = 12 cm. Step 5: Length = 12 + 3 = 15 cm. Step 6: Area = length × width = 15 × 12 = 180 cm². Therefore, the area is 180 cm².

Question 11

A square and a rectangle have the same perimeter of 48 cm. The rectangle's length is 14 cm. What is the difference between the area of the square and the area of the rectangle?

Accepted Answer

Step 1: For the square: Perimeter = 48 cm, so 4 × side = 48, therefore side = 12 cm. Area of square = 12² = 144 cm². Step 2: For the rectangle: Perimeter = 48 cm, length = 14 cm. Using 2(length + width) = 48, we get 2(14 + width) = 48, so 14 + width = 24, therefore width = 10 cm. Step 3: Area of rectangle = 14 × 10 = 140 cm². Step 4: Difference = 144 − 140 = 4 cm². Therefore, the difference is 4 cm².

Question 12

A parallelogram has sides of 20 cm and 15 cm. The angle between them is 60°. What is the area of the parallelogram?

Accepted Answer

Step 1: Area of parallelogram = side₁ × side₂ × sin(angle between them). Step 2: Area = 20 × 15 × sin(60°). Step 3: sin(60°) = √3/2 ≈ 0.866. Step 4: Area = 20 × 15 × (√3/2) = 300 × (√3/2) = 150√3 cm². Step 5: 150√3 ≈ 150 × 1.732 = 259.8 ≈ 260 cm². Therefore, the area is approximately 260 cm² or 150√3 cm².

SSC GD Constable Quadrilaterals

Quadrilaterals— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Quadrilaterals — Practice Questions

60-Second Revision — Quadrilaterals