Question

PLEASE HELP! I will award Brainliest!!! Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

Answer:

125.66sq.in

Step-by-step explanation:

Area of the circle is π$r^{2}$= π x 10 x 10 = 314.159 sq.in

Area of the shaded area is = (314.159/360) x (72+72) = 125.44

Answer 2

Answer:

40$\pi$ or 125.66$inches^2$

Step-by-step explanation:

The formula for the area of the circle is : $\pi*radius^2$

To work this out you would first need to work out the area. You can do this by multiplying pi by the radius of 10 squared, this gives you .

Now that we have worked out the area we now work out the area in 1° of the circle. You can do this by dividing the area of 100$\pi$ or 314.16 by 360, this gives you $\frac{5}{18}\pi$ or . This is because the total angle in a circle is 360°.

Now that we have worked out the area per degree of the circle we can now work out the total angle of the shaded region. You can do this by adding the angles of 72 and 72, this gives you 144. This is because we are working out the total of the two given values.

The final step is to multiply the area per angle of  $\frac{5}{18}\pi$ or 0.87 by the total angle of the shaded region of 144, this gives you 40$\pi$ or 125.66$inches^2$

1) Multiply pi by 10 squared.

$\pi*10^2=100\pi or 314.16$

2) Divide 100$\pi$ or 314.16 by 360.

$100\pi or 314.16/360=\frac{5}{18}\pi or 0.87$

3) Add 72 and 72.

$72+72=144$

4) Multiply $\frac{5}{18}\pi$ or 0.87 by 144.

$\frac{5}{18}\pi*or 0.87*144=40\pi or125.66inches^2$