Q. 104.7( 27 Votes )

# A park, in the shape of a quadrilateral ABCD, has ∠C = 90˚, AB = 9m, BC = 12 m, CD = 5m and AD = 8m. How much area does it occupy?

Given: C = 90˚, AB = 9m, BC = 12 m, CD = 5m and AD = 8m.

To Find: Area of quadrilateral ABCD.

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Area of a right-angled triangle

Diagram:

Explanation:

Area of park = Area of ΔBCD + Area of ΔABD

ΔBCD is a right-angled triangle. Therefore,

Area of ΔBCD = 1/2 × 12 × 5 m2 = 30 m2

InΔ ABD, we have

2s = 9 + 8 + 13 = 30 s = 15

= 6√35 m2

Area of park = (30 + 6√35) cm2

Hence, the area of the park is (30 + 6√35) cm2.

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