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
![A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B5%5Cleft%285%2B2%5Csqrt%7B5%7D%5Cright%29%7Da%5E2%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A)
![A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(7\right)^2\:\:\:\:\:\:](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B5%5Cleft%285%2B2%5Csqrt%7B5%7D%5Cright%29%7D%5Cleft%287%5Cright%29%5E2%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A)
![A\approx 84.3\:\:\:](https://tex.z-dn.net/?f=A%5Capprox%2084.3%5C%3A%5C%3A%5C%3A)
Thus,
The Area of the Blue Pentagon = ![A\approx 84.3\:\:\:](https://tex.z-dn.net/?f=A%5Capprox%2084.3%5C%3A%5C%3A%5C%3A)
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
![A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B5%5Cleft%285%2B2%5Csqrt%7B5%7D%5Cright%29%7Da%5E2%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A)
![A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(4\right)^2\:\:\:\:\:\:](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B5%5Cleft%285%2B2%5Csqrt%7B5%7D%5Cright%29%7D%5Cleft%284%5Cright%29%5E2%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A)
![\:A\approx 27.5](https://tex.z-dn.net/?f=%5C%3AA%5Capprox%2027.5)
The Area of the Red Pentagon = ![\:A\approx 27.5](https://tex.z-dn.net/?f=%5C%3AA%5Capprox%2027.5)
<u><em>Conclusion:</em></u>
The Perimeter of the Blue Pentagon = 35
The Perimeter of the Red Pentagon = 20
Thus, the<u><em> ratio of the perimeter</em></u> 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<u><em> ratio of the Area</em></u> is:
![\frac{\frac{843}{10}}{\frac{275}{10}}=\frac{843}{275}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B843%7D%7B10%7D%7D%7B%5Cfrac%7B275%7D%7B10%7D%7D%3D%5Cfrac%7B843%7D%7B275%7D)