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Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

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550m 2

660 m 2

66 m 2

6 m 2

answer is B.

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Detailed Solution

It is given Length of the fence of a trapezium-shaped field ABCD is 120 m.
And length of the sides is given as

and

Therefore, Perimeter of trapezium

A B C D = A B + B C + C D + D A

⇒ 120 = A B + 48 + 17 + 40 ⇒ 120 = A B + 105 ⇒ A B = 120 − 105 ⇒ A B = 15

The area of trapezium is given as.
Area of trapezium

= 12 (a + b) × h

Where, a = one of the parallel sides,
b = another parallel side,
h = height
Area of the trapezium is;

⇒ 12 (B C + A D) × A B

⇒ 12 (48 + 40) × 15

⇒ 12 × 88 × 15

⇒ 660 m 2

Hence option (2) is correct.

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