Worksheet on Area of Trapezium

Slanted sides and parallel bases form interesting four-sided shapes. Young mathematicians work with areas of trapezium printable practice questions that explore the special formula combining parallel sides and height measurements. These challenging activities guide students through step-by-step calculations while connecting trapezoids to architectural designs and natural formations. Students can download a free area of a trapezium worksheet PDF; every solution builds geometric reasoning skills effectively.

1. What is the area of a trapezium with bases of 10 cm, 14 cm and a height of 5 cm?

a) 60 cm²
b) 120 cm²
c) 100 cm²
d) 80 cm²

Answer: a)

Explanation: Area of trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ (a + b) × h
                                                     = $\frac{\frac{1}{}}{\frac{2}{}}$ (10 cm + 14 cm) × 5 cm
                                                     = 60 cm²

2. A trapezium’s bases are 8 cm and 5 cm respectively and the area is 52 cm². What is the height of the trapezium?

a) 7 cm
b) 13 cm
c) 8 cm
d) 10 cm

Answer: c)

Explanation: Area of trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ × (a + b) × h
52 = $\frac{\frac{1}{}}{\frac{2}{}}$ x (8 + 5) x h
52 = $\frac{\frac{1}{}}{\frac{2}{}}$ x 13 x h
h = 8 cm

Hence, height of the trapezium = 8 cm

3. A trapezium has a height of 7 cm and one of the parallel sides is longer than the other by 8 cm. If the area is 91 cm², what is the length of the longer side?

a) 9 cm
b) 13 cm
c) 17 cm
d) 10 cm

Answer: c)

Explanation: Let a = x cm, b = (x + 8) cm
Area of trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ × (x + (x + 8)) × 7
91 cm² = $\frac{\frac{7}{}}{\frac{2}{}}$ × (2x + 8) cm²
26 = 2x + 8
x = 9
Now, b = x + 8 = 9 + 8 = 17 cm

Hence, length of longer side is 17 cm.

4. Determine the length of the longer parallel side of a trapezium-shaped field given that its area is 60 m² and the height between the parallel sides is 12 m. The difference between the lengths of the two parallel sides is 4 m.

a) 13 cm
b) 7 cm
c) 3 cm
d) 5 cm

Answer: b)

Explanation: Let's denote the length of the shorter side as ‘a’ and the longer side as ‘b’.
ATQ, b - a = 4
b = a + 4
We know that area of trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ × (a + b) × h
60 = $\frac{\frac{1}{}}{\frac{2}{}}$ × (a + a + 4) × 12
10 = 2a + 4
a = 3

Thus, b = 3 + 4 = 7 cm
Length of the longer side = 7 cm.

5. The parallel sides of a trapezium are in the ratio 4 : 3 and the distance between them is 10 m. If the area of the trapezium is 350 m², find the shorter parallel side of the trapezium.

a) 20 cm
b) 40 cm
c) 15 cm
d) 30 cm

Answer: d)

Explanation: Let the lengths of the parallel sides be a and b.
As the ratio is 4 : 3, we can express a = 4x and b = 3x.
Plug all the values into the area formula:
A = $\frac{\frac{1}{}}{\frac{2}{}}$ × (a + b) × h
350 = $\frac{\frac{1}{}}{\frac{2}{}}$ x (4x + 3x) x 10
  70 = 7x
    x = 10
Now, b = 3x = 3 x 10 = 30 m

Therefore, the length of the shorter parallel side of the trapezium is 30 m.

6. A garden bed is in the shape of a trapezium with bases of 10 m, 6 m and a height of 4 m. If another trapezium-shaped bed with the same height has bases of 8 m and 7 m, what is the total area of both garden beds?

a) 64 m²
b) 68 m²
c) 62 m²
d) 76 m²

Answer: c)

Explanation: Area of the first trapezium A₁ = $\frac{\frac{1}{}}{\frac{2}{}}$ x (Sum of parallel sides) x height
                                                                        = $\frac{\frac{1}{}}{\frac{2}{}}$ (10 + 6) x 4
                                                                        = 32 m²
Area of the second trapezium A₂ = $\frac{\frac{1}{}}{\frac{2}{}}$ (8 + 7) x 4               
                                                     = 30 m²
Total area = 32 m² + 30 m²
                 = 62 m²

7. A trapezium has bases of 25 m and 15 m and a height of 10 m. If another trapezium with the same bases has its height increased by 5 m, what is the difference in the areas of the two trapeziums?

a) 50 m²
b) 75 m²
c) 100 m²
d) 125 m²

Answer: c)

Explanation: Area of the first trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ x (25 + 15) x 10 = 200 m²
Area of the second trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ x (25 + 15) x 15 = 300 m²
Difference in areas = 300 m² - 200 m²
                               = 100 m²

8. A piece of land in the shape of a trapezium has bases of 30 m, 20 m and a height of 10 m. If a triangular section with a base of 15 m and a height of 10 m is removed, what is the remaining area?

a) 175 m²
b) 285 m²
c) 290 m²
d) 300 m²

Answer: a)

Explanation: Area of the trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ x (30 + 20) x 10 = 250 m²
Area of the triangular section = $\frac{\frac{1}{}}{\frac{2}{}}$ x 15 x 10 = 75 m²
Area of the remaining section = 250 m² - 75 m²
                                                 = 175 m²

9. A trapezium has bases of 12 m, 18 m and a height of 9 m. If an equilateral triangle with a side length of 6 m is removed from this trapezium, what is the remaining area of the trapezium? (Use √3 = 1.732)

a) 119.4 m²
b) 135.5 m²
c) 140.5 m²
d) 145.5 m²

Answer: a)

Explanation: Area of a trapezium = $\frac{\frac{1}{}}{\frac{2}{}}$ x (12 + 18) x 9 = 135 m²
Area of the equilateral triangle = √34 x 6 x 6 = 15.588 ≈ 15.6 m²
Area of the remaining portion = 135 m² - 15.6 m²
                                                = 119.4 m²

10. A farmer wants to cover two adjacent trapezium-shaped fields with fertiliser. The first field has bases of 18 m and 12 m and a height of 5 m. The second field has bases of 20 m and 10 m and a height of 7 m. What is the total area to be covered?

a) 175 m²
b) 180 m²
c) 195 m²
d) 205 m²

Answer: b)

Explanation: Area of the first field = $\frac{\frac{1}{}}{\frac{2}{}}$ x (12 + 18) x 5 = 75 m²
Area of the second field = $\frac{\frac{1}{}}{\frac{2}{}}$ x (20 + 10) x 7 = 105 m²
Total area = 75 m² + 105 m²
                 = 180 m²