Question

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

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

$A=\frac{5}{2} (a)(s).$

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

The area of a pentagon $= \frac{5}{2} (5.5)(8) = 110$ 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.