Question

PLEASE HELP, 30 points AND brainliest if I get an explanation :)

Answer 1

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

 $A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:$

$A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(7\right)^2\:\:\:\:\:\:$

$A\approx 84.3\:\:\:$

Thus,

The Area of the Blue Pentagon = $A\approx 84.3\:\:\:$

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

 $A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:$

$A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(4\right)^2\:\:\:\:\:\:$

$\:A\approx 27.5$

The Area of the Red Pentagon = $\:A\approx 27.5$

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:

 $\frac{\frac{843}{10}}{\frac{275}{10}}=\frac{843}{275}$