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
[tex]A=\frac{5}{2} (a)(s).[/tex]
In the given diagram, the pentagons have side lengths of 8 units and an apothem of 5.5 units.
The area of a pentagon [tex]= \frac{5}{2} (5.5)(8) = 110[/tex] sq units.
The area of 2 such pentagons [tex]= 2(110)= 220[/tex] square units.
The rectangle has a length of 14 units and a width of 8 units.
The area of a rectangle [tex]= (l)(w).[/tex]
The area of the rectangle [tex]= (14)(8)=112[/tex] 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 [tex]=220+112=332[/tex] sq units.
The area of the composite shape is option A. 332 sq units.
