Question

The base of a regular pyramid is a hexagon.

Answer 1

Answer:

96$\sqrt{3}$ cm²

Step-by-step 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° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{a}{8}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2a = 8$\sqrt{3}$ ( divide both sides by 2 )

a = 4$\sqrt{3}$ cm

The area (A) can be calculated using

A = $\frac{1}{2}$ 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 = $\frac{1}{2}$ × 48 × 4$\sqrt{3}$ = 96$\sqrt{3}$ cm²