Question

The base of a regular pyramid is a hexagon.

Answer 1

96
`√(3)` cm²

Explanation:

A hexagon can be cut into 6 equilateral triangles.

Using the half shown in the diagram to calculate the apothem a , and the exact value

sin60° =
`(√(3) )/(2)` , then

sin60° =
`(opposite)/(hypotenuse)` =
`(a)/(8)` =
`(√(3) )/(2)` ( cross- multiply )

2a = 8
`√(3)` ( divide both sides by 2 )

a = 4
`√(3)` cm

The area (A) can be calculated using

A =
`(1)/(2)` pa ( p is the perimeter of the hexagon )

The sides of the hexagon measure 8 cm ( equilateral Δ has congruent sides )

p = 6 × 8 = 48 cm, so

A =
`(1)/(2)` × 48 × 4
`√(3)` = 96
`√(3)` cm²