Question

find the area of the shaded region. give your answer as a completely simplified exact value in terms of π (no approximations)

Answer 1

7pi

Explanation:

The formula for the area of a circle is pr^2 the radius of the large circle is two. Substituiting we get pi3^2 or 9pi using the same formula we can find the areas of the smaller triangles are both 1pi each. Subtracting the unshaded from the shaded we get 7pi

Answer 2

Area of the shaded region is 7π

Explanation:

To find the area of the shaded region; Will find the area of the entire circle, then find the area of the two smaller circle, we will then subtract the two areas of the smaller circle from area of the entire circle.

Area of a circle is πr²

The radius of the entire circle is 3,

then area of the entire circle =π(3)² =9π

The radius of the first small circle is 1

then the area of the small circle is π(1)² =π

The second circle is having the same radius as the first one, then the area will be the same as the first one, that is its area is also π

Area of the shaded region = Area of the entire circle - area of the first small circle - area of the second small circle

Area of the shaded region =9π - π - π

=7π

Therefore area of the shaded region is 7π