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

# Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm,    and BC = CD = 52 cm.

1. A
2. B
3. C
4. D

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### Solution:

Let the diagram of the situation be,
Given that, AB = 32 cm, AD = 24 cm,    and BC = CD = 52 cm.
Apply the Pythagoras theorem, find the value of BD, and we have

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

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

The area of the triangle is given by,

Hence, the area of the quadrilateral is given by,

Hence, the correct option is 1.

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