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A triangle is placed in a semicircle with a radius of 9 ft, as shown below. Find the area of the shaded region.

Use the value of 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.

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00:52

The circle with center $D$ is drawn inside the circle with center $C,$ as shown in the figure above. If $C D=3,$ what is the area of semicircle $E A B ?$a. $$\frac{9}{2} \pi$$b. $$9 \pi$$c. $$12 \pi$$d. $$18 \pi$$e. $$36 \pi$$

01:06

Find the area of the shaded region. Use 3.14 for $\pi .$ Include the correct units. (FIGURE CAN’T COPY)

03:00

Find the area of the shaded region. Use 3.14 for $\pi .$ Include the correct units. (FIGURE CAN’T COPY)

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Transcript

So in the given question we are told to find the area of the shaded region of a figure where the figure is a semi circle. And in the semi circle we have a triangle. Right? And we are told that the height of the strangle is nine ft. Right? So the height of this triangle would be the radius of the semicircle as well. Right? So we can write this is the height of the triangle height of the triangle and also the radius of the semicircle. So now the shaded region that has given the figure is this part over here. So what we would do is we would first find the area of the semi circle and then the area of the triangle, and we would subtract the area of the triangle from the semicircle. So first let’s write the formula for finding the area of a semicircle. So what you should know about a semicircle is that it is half of a circle, so it would be half the area of a circle. Right? So the area of a circle is given by the formula pi R squared. So the area of a semicircle would be half this area. So now we already have told that the radius of the semicircle as nine ft. So we can write half times pi times r squared, would be Instead of pie. Let’s ride the value of Pi, which is 3.14. And for our we can write nine. So 9 squared. So now when we take one by two times 3.14 times nine squared. What we get as the area of the…

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