Question

. A park is in the shape of a quadrilateral ABCD in which AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. If angleC =90degree , find the area of the park

Answer 1

Answer:

65.5 m²

Step-by-step explanation:

Given, ABCD is a quadrilateral with ∠C = 90°.

Join BD, we get a diagonal.

(i) Area of ΔBCD:

= (1/2) * base * height

= (1/2) * 5 * 12

= 30 m².

In ΔBCD,

BD² = BC² + CD²

      = 12² + 5²

      = 169

BD = 13 m.

(ii) Area of ΔABD:

a = 9 m, b = 8 m, c = 13 m.

Semi-perimeter s = (a + b + c)/2 = 15 m.

∴ Area = √s(s - a)(s - b)(s - c)

           = √15 * 6 * 7 * 2

           = √1260 m²

           = 6√35

          = 35.5 m²

(iii) Area of the park:

Area of ΔBCD + Area of ΔABD

= 30 + 35.5

= 65.5 m²

∴ The park occupies the area 65.5 m².

Hope it helps!