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?

Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures x√3 units and the hypotenuse measures 2x units.


(150√3 - 75π) ft^2

(300 – 75π) ft^2

(150√3 – 25π) ft^2

(300 – 25π) ft^2

Answer 1

Option A. (150√3- 75π) ft².

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(√(3) )/(2)(side)^(2)`

=
`=3(√(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 =
`(10)/(2)√(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

Answer 2

Answer: its A

(150 – 75π) ft2