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=(1)/(2)*\text{base}*\text{height}`

Area of triangle DAC:

`$A=(1)/(2)* AC * DE`

`$A=(1)/(2)* 12 * 4`

`A=24`

Area of triangle DAC = 24 square units.

Area of triangle BAC:

`$A=(1)/(2)* AC * FB`

`$A=(1)/(2)* 12 * 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.