Question

Find the area of the hexagon. i will mark brainliest and pls explain.

Answer 1

Answer:

• C. 150√3

Step-by-step explanation:

Radius of the inscribed circle is the apothem of the hexagon.

Apothem (a) and half of the side (s) make a 30-60-90 right triangle.

The ratio of the legs, as per property of 30-60-90 triangle:

• s : a = 1 : √3 ⇒ s : 5√3 = 1 : √3 ⇒ s = 5

Half the side is s = 5 units, then side of the hexagon is 10 units.

The area of the hexagon:

• A = 1/2Pa, P- perimeter, a- apothem
• A = 1/2(6*10)*(5√3) = 150√3

Correct choice is C