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2 years ago

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

Mathematics

1 answer:

Vika [28.1K]2 years ago

4 0

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

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