Question

Find the area of the following polygon:

Answer 1

Given:

ABCD is a quadrilateral

AC = 12, DE = 4 and FB = 5

To find:

The area of the polygon.

Solution:

AC bisects the quadrilateral into two triangles.

Area of triangle:

$A=\frac{1}{2}\times\text{base}\times\text{height}$

Area of triangle DAC:

$A=\frac{1}{2}\times AC \times DE$

$A=\frac{1}{2}\times 12 \times 4$

$A=24$

Area of triangle DAC = 24 square units.

Area of triangle BAC:

$A=\frac{1}{2}\times AC \times FB$

$A=\frac{1}{2}\times 12 \times 5$

$A=30$

Area of triangle BAC = 30 square units.

Area of polygon = Area of triangle DAC + Area of triangle BAC

                           = 24 square units + 30 square units

                           = 54 square units

The area of the polygon is 54 square units.