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Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, $∠ A = 90 ∘$ and BC = CD = 52 cm.

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answer is A.

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Detailed Solution

Let the diagram of the situation be,
seo

Given that, AB = 32 cm, AD = 24 cm,

∠ A = 90 ∘

and BC = CD = 52 cm.
Apply the Pythagoras theorem, find the value of BD, and we have

B D 2 = A B 2 + A D 2 B D 2 = 322 + 242 B D = 1600 B D = 40 c m

The area of the right-angled triangle ABD is given by,

A A B D = 12 × A B × A D = 12 × 32 × 24 = 384 c m 2

To find the area of the other triangle ACD, its perimeter is half of the perimeter.

s = P 2 = a + b + c 2 = 52 + 52 + 40 2 = 1442 = 72 c m

The area of the triangle is given by,

A A C D = s (s − a) (s − b) (s − c) = 72 (72 − 52) (72 − 52) (72 − 40) = 72 (20) (20) (32) = 960 c m 2

Hence, the area of the quadrilateral is given by,

A = A A B D + A A C D = 384 + 960 = 1344 c m 2

Hence, the correct option is 1.

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