Answer:
42 sq. un.
Step-by-step explanation:
Consider pentagon GPEST. The area of this pentegon consists of the sum of the area of the rectangle GPST and the area of the triangle PES.
1. The rectangle GPST has sides lengths of 5 un. and 7 un.. Thus, the area of the rectangle GPST is
[tex]A_{GPST}=7\cdot 5=35\ un^2.[/tex]
2. The area of the triangle PES can be calculated as
[tex]A_{PES}=\dfrac{1}{2}\cdot PS\cdot h,[/tex]
where h is the height drawn to the side PS. Since PS=7 un., then
[tex]A_{PES}=\dfrac{1}{2}\cdot 7\cdot 2=7\ un^2.[/tex]
Therefore,
[tex]A_{GPEST}=A_{GPST}+A_{PES}=35+7=42\ un^2.[/tex]
