Question

The base of a regular pyramid is a hexagon.

What is the area of the base of the pyramid?

Enter your answer in the box. Express your answer in radical form.

Answer 1

The triangle in the drawing is semi equilateral. Therefore a=√(14^2-7^2)=12.12 cm
The base of a regular pyramid consists of 6 equilateral triangles. The area of each triangle is: (14*12.12)/2 = 84.87 cm^2
The base: 6*84.87=509.22 cm^2

Answer 2

Answer: Area of the base of the pyramid
`=294√(3)\text{ cm}^2`

Explanation:

Since we have given that

The base of a regular pyramid is a hexagon.

so, hexagon must be regular too.

We need to find the area of the base of the pyramid i.e. area of hexagon.

As we know that there are 6 equilateral triangles in a hexagon.

And length of each side = 14 cm

As we know the formula for "Area of equilateral triangle":

`Area=(√(3))/(4)* a^2`

so, Area of base of the pyramid is given by

`6* (√(3))/(4)\tiems a^2\\\\=6* (√(3))/(4)* 14* 14\\\\=294√(3)\text{ cm}^2`