Question

The composite figure is made up of a rectangle and two pentagons. Find the

area
O
A. 332 sq. units
B. 290 sq. units
O
C. 200 sq units
D. 552 sq units

Answer 1

Given:

A composite figure made up of a rectangle and two pentagons.

To find:

The area of the composite shape.

Solution:

If a pentagon has a side length of s and an apothem of a, the area of the pentagon is given by

`A=(5)/(2) (a)(s).`

In the given diagram, the pentagons have side lengths of 8 units and an apothem of 5.5 units.

The area of a pentagon
`= (5)/(2) (5.5)(8) = 110` sq units.

The area of 2 such pentagons
`= 2(110)= 220` square units.

The rectangle has a length of 14 units and a width of 8 units.

The area of a rectangle
`= (l)(w).`

The area of the rectangle
`= (14)(8)=112` square units.

The area of the composite shape is the sum of the individual areas of the different shapes.

The area of the composite shape
`=220+112=332` sq units.

The area of the composite shape is option A. 332 sq units.