Q10 of 33 Page 12

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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