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

Question

A park, in the shape of a quadrilateral ABCD, has &#x2220; C = 90&#xB0;, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

Philoid · Accepted Answer

Given: The figure is given below:

The dimensions of the park as follows:

Angle C = 90⁰,

AB = 9m,

BC = 12m,

CD = 5m

And, AD = 8m

Now, BD is joined.

In by Pythagoras theorem,

BD² = BC² + CD²

BD² = 12² + 5²

BD² = 169

BD = 13m

Now, Semi perimeter of triangle (ABD) =

= 13/2 = 15m

Using Heron’s formula,

Area of =

=

= m²

= 35.5 m² (approx.)

Area of quadrilateral ABCD = Area of

= 30 + 35.5

= 65.5 m²

Thus, the park acquires an area of 65.5 m²