Answer:
Please check the explanation.
Step-by-step explanation:
BLUE PENTAGON
The blue shape represents the Pentagon
The length of the side a = 7
As there are 5 sides.
Thus,
The Perimeter of the Blue Pentagon = P = 5a = 5(7) = 35
Using the formula to determine the area of the Pentagon
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:[/tex]
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(7\right)^2\:\:\:\:\:\:[/tex]
[tex]A\approx 84.3\:\:\:[/tex]
Thus,
The Area of the Blue Pentagon = [tex]A\approx 84.3\:\:\:[/tex]
RED PENTAGON
The red shape represents the Pentagon
The length of the side a = 4
As there are 5 sides.
Thus,
The Perimeter of the Red Pentagon = P = 5a = 5(4) = 20
Using the formula to determine the area of the Pentagon
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:[/tex]
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(4\right)^2\:\:\:\:\:\:[/tex]
[tex]\:A\approx 27.5[/tex]
The Area of the Red Pentagon = [tex]\:A\approx 27.5[/tex]
Conclusion:
The Perimeter of the Blue Pentagon = 35
The Perimeter of the Red Pentagon = 20
Thus, the ratio of the perimeter is: 35/20 = 7/4
The Area of the Blue Pentagon = 84.3 = 843/10
The Area of the Red Pentagon = 27.5 = 275/10
Thus, the ratio of the Area is:
[tex]\frac{\frac{843}{10}}{\frac{275}{10}}=\frac{843}{275}[/tex]
