Question

Find the total area the regular pyramid.

Answer 1

The total area of the regular pyramid would be = 16√3.

How to calculate the total area of the regular pyramid?

To calculate the total area of the regular pyramid, the following steps should be taken as follows:

The area of regular pyramid is the sum of base area and the area of all sides.

From the given figure it is clear that it is a regular pyramid with side length 4 units. All sides and base are equilateral triangles of side 4 units.

The area of an equilateral triangle:

= √¾(a)²

where;

a = 4

That is;

= √¾(4)²

= 16√¾

= 4√3

There are 4 equilateral triangles,

total area of the pyramid:

= 4×4√3

= 16√3

Answer 2

The area of the regular pyramid is 16√3 square units.

Explanation:

The area of regular pyramid is the sum of base area and the area of all sides.

From the given figure it is clear that it is a regular pyramid with side length 4 units. All sides and base are equilateral triangles of side 4 units.

The area of an equilateral triangle is

`A=(√(3))/(4)a^2`

Where, a is the side length.

Substitute a=4 to find the area of base is

`Base=(√(3))/(4)(4)^2=(16√(3))/(4)=4√(3)`

The given figure contain 4 equilateral triangles of side 4 units. So the area of regular pyramid is

`A=4* Base=4* 4√(3)=16√(3)`

Therefore the area of the regular pyramid is 16√3 square units.