Question

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

Answer 1

Here, AB = 9 m, BC = 12 m, CD = 5 m, DA = 8 m.

And BD is a diagonal of ABCD. 

In right △BCD,

From Pythagoras theorem; 

BD² = BC² + CD² 

BD² = 12² + 5² 

= 144 + 25

= 169

BD = 13 m 

Area of △BCD = 1/2 x BC x CD

= 1/2 x 12 x 5 

= 30

Area of △BCD = 30 m² 

Now, In △ABD, 

All sides are known, Apply Heron’s Formula:

Where a, b and c are sides of a triangle.

Perimeter of △ABD = 2s = 9 m + 8m + 13m

 s = 15 m

Area of the △ABD = 35.49 m² 

Area of quadrilateral ABCD = Area of △ABD + Area of △BCD 

= (35.496 + 30) m²

= 65.5 m²