Question

Find the area of the shaded region. Round your answer to the nearest tenth. Put the units on the answer for full credit. Use the calculator pi button. photo attached

Answer 1

Answer:

Area of Shaded Region: ( About ) 19.6

Step-by-step explanation:

~ To find the area of the shaded region, let us calculate the area of the circle, and the area of the hexagon, subtracting it's area from the area of the circle ~

1. Given a radius of 6 cm, let us calculate the area of the circle provided the area formula πr^2. Substitute the value of the radius, but keep π in terms of π until the end ⇒ π * ( 6 )^2 = 36π ⇒ ( About ) 113.1 units^2

2. To find the area of the hexagon, let us divide the hexagon into 6 triangles. All 3 of the sides of each triangle is 6 cm, provided these are equilateral triangles. We should calculate the area of each triangle, so let us draw an altitude for each of these Δs. Doing so, through Coincidence Theorem we split the segment drawn to the altitude into two ≅ parts, or 3 units each. That means that the altitude must be 3√3, by properties of 60-60-60 triangles. That being said, the area of one of the triangles: 1/2 * base * height ⇒ 1/2 * 6 * 3√3 ⇒ 9√3 units^2.

3. Knowing that all the 6 triangles are ≅, let us simply multiply the area of a of the triangles * 6 to recieve the area of the hexagon ⇒ 9√3 * 6       ⇒ 54√3 units^2

4. The area of the shaded region is now ⇒ 113.1 - 54√3 ⇒

Area of Shaded Region: ( About ) 19.6