Question

Pleeeeeease help. !! !!!!!

Answer 1

259.8 cm²

Explanation:

A regular hexagon can be cut into 6 equilateral triangles and an equilateral triangle can be divided into two 30°- 60°- 90° triangles

Note that the apothem (5
`√(3)`) divides the triangle into two equilateral triangles, thus

The apothem is the long leg (the x
`√(3)`) side of a 30- 60- 90 triangle, so

x
`√(3)` = 5
`√(3)` ⇒ x = 5

Thus the side length of the hexagon = 2 × 5 = 10

and the perimeter = 6 × 10 = 60

A =
`(1)/(2)` × perimeter × apothem

= 0.5 × 60 × 5
`√(3)` = 150
`√(3)` ≈ 259.8 cm²