Question

The answer is A. A circle is inscribed in a regular hexagon with side length 10 feet. What is the area of the shaded region?

Answer 1

Answer: its A

(150 – 75π) ft2

Answer 2

Answer:

Option A. (150√3- 75π) ft².

Step-by-step explanation:

In the given picture a circle is inscribed in a regular hexagon with a side length = 10 feet.

Formula of the area of a regular hexagon $=3\frac{\sqrt{3} }{2}(side)^{2}$

                                                              = $=3\frac{\sqrt{3} }{2}(10^{2})$

                                                             = 3√3×50 = 150×√3 feet²

Now we will calculate the area of circle inscribed.

Already given in the question that In a 30-60-90 triangle

Longer leg of triangle r = x√3 = $\frac{10}{2}\sqrt{3}$ = 5√3 feet

Now area of circle = π r² = π(5√3)² = 75π feet²

Area of shaded part = Area of Hexagon-Area of circle inscribed.

                                 = (150√3 - 75π) ft²