Question

The base of a regular pyramid is a hexagon.
What is the area of the base of the pyramid?

Express your answer in radical form.

Answer 1

Answer:

96sqrt(3)

Step-by-step explanation:

Simplest and most intuitive way is to find area of 1 triangles and multiply it by 6.

Area of one triangle:

base = 8 and a = 4sqrt(3)

Area of 1 trangle = ba/2

Area of base of hexagon = 6 times that.

Answer 2

Answer:

$72\sqrt{3} cm^2$

Step-by-step explanation:

We are given that the base of a regular pyramid is a hexagon and we are to find the area of the base (which is a hexagon).

We know that the formula for the area of hexagon is given by:

$A = \frac { 3 \sqrt { 3 } } { 2 } a^2$

We are to find the value of a to find this area.

Finding a:

$sin 60=\frac{a}{8}$

$a=6.92$

Substituting this value of $a$ in the above formula to get:

Area of the base (hexagon) = $\frac { 3 \sqrt { 3 } } { 2 } \times 48 (6.92)^2$ = $72\sqrt{3} cm^2$