# Mathematics Questions and Answers – Mensuration – Area of Trapezium – 2

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This set of Mathematics Aptitude Test for Class 8 focuses on “Mensuration – Area of Trapezium – 2”.

1. Find the area of the given figure. (π = 3.14) a) 26m2
b) 13.28m2
c) 26.28m2
d) 27.28m2

Explanation: Area of the given figure = Area of square + 2 × semicircle + 2 × triangle = (4)2 + π $$\frac{(2)^2}{2} + \frac{1}{2}$$ × 4 × 2 = 26.28m2.

2. What is the area of the given figure? (π = $$\frac{22}{7}$$) a) 70m2
b) 35m2
c) 74m2
d) 60m2

Explanation: Area = Area of rectangle – Area of circle = l × b – π(r)2 = 16 × 14 – $$\frac{22}{7}$$ (7)2 = 70m2.

3. Find the area and perimeter of the given trapezium, respectively. a) 30m2, 15m
b) 15m2, 30m
c) 15m2, 15m
d) 30m2, 30m

Explanation: Area of trapezium = $$\frac{1}{2}$$ × (p1 + p2) × h  [(p1 + p2) = Σ of ∥sidesoftrapezium]
= $$\frac{1}{2}$$ × (8 + 12) × 3 = 30m2
Perimeter = 4 + 8 + 6 + 12 = 30m.
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4. Calculate the area of the given figure. a) 7cm2
b) 7.5cm2
c) 6.5cm2
d) 8cm2

Explanation: Area of general quadrilateral = $$\frac{1}{2}$$ × (h1 + h2) × d  [d is the length of diagonal]
= $$\frac{1}{2}$$ × (1 + 1.5) × 6 = 7.5cm2.

5. The Area of trapezium shaped garden is 225m2. The distance between the two parallel sides is 25m. The length of one parallel side is 11m, what is the length of the other parallel side?
a) 7m
b) 8m
c) 6m
d) 5m

Explanation: Area of trapezium = $$\frac{1}{2}$$ × (p1 + p2) × h  [(p1 + p2) = Σ of ∥ sidesoftrapezium]
⇒ 225m2 = $$\frac{1}{2}$$ × (11 + p2) × 25
⇒ p2 = 7m.

6. The Area of trapezium is 800m2. The lenghts of the parallel sides is 28mand 12m. Find the height of the trapezium.
a) 22m
b) 42m
c) 40m
d) 20m

Explanation: Area of trapezium = $$\frac{1}{2}$$ × (p1 + p2) × h  [(p1 + p2) = Σ of ∥ sidesoftrapezium]
⇒ 800m2 = $$\frac{1}{2}$$ × (28 + 12) × h
⇒ h = 40m.

7. In a trapezium shaped ground, there is a square shaped lawn. The side of the lawn is 12m. The length of the parallel sides is 24m and 40m.The height of the ground is 30m. Find the area of the shaded portion. a) 806m2
b) 336m2
c) 1776m2
d) 816m2

Explanation: Area of the shaded portion = Area of trapezium(ground) – Area of square(lawn)
= $$\frac{1}{2}$$ × (p1 + p2) × h – (s)2 = $$\frac{1}{2}$$ × (40 + 24) × 30 – (12)2 = 816m2.

8. Find the area of the given Figure. a) 42m2
b) 24m2
c) 14m2
d) 7m2

Explanation: Area = Area of trapezium + Area of triangle = $$\frac{1}{2}$$ × (p1 + p2) × h + $$\frac{1}{2}$$ × b × h
= $$\frac{1}{2}$$ × (5 + 3) × 2 + $$\frac{1}{2}$$ × 4 × 3 = 14cm2.

9. What is the area of the given figure? a) 10cm2
b) 13cm2
c) 12cm2
d) 11cm2

Explanation: Area = Area of trapezium 1 + Area of trapezium 2
= $$\frac{1}{2}$$ × (p1 + p2) × h1 + $$\frac{1}{2}$$ × (p3 + p4) × h2 = $$\frac{1}{2}$$ × (2 + 4) × 2 + $$\frac{1}{2}$$ × (3 + 4) × 2 = 13cm2.

10. Find length of AE if area of the given figure is 15cm2. a) 9 cm
b) 8 cm
c) 7 cm
d) 6 cm

Explanation: Area of given figure = Area of trapezium + Area of triangle
⇒ 15cm2 = $$\frac{1}{2}$$ × (p1 + p2) × h1 + $$\frac{1}{2}$$ × b × h
⇒ 15cm2 = $$\frac{1}{2}$$ × (4 + 2) × 2 + $$\frac{1}{2}$$ × b × 2
⇒ b = 9 cm
⇒ length (AE) = 9 cm.

11. Compare the area of given trapezium. a) B > A
b) B < A
c) B = A = 7cm2
d) B = A = 9cm2

Explanation: Area of A = $$\frac{1}{2}$$ × (p1 + p2) × h1 = $$\frac{1}{2}$$ × (3 + 4) × 2 = 7cm2
Area of B = $$\frac{1}{2}$$ × (p1 + p2) × h1 = $$\frac{1}{2}$$ × (4 + 2) × 3 = 9cm2
⇒ Area of B > Area of A.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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