Question

Rafael is cutting pieces of wood to make a triangular pyramid like the one shown below. The base of the pyramid is an equilateral triangle, and the faces are isosceles triangles.

Answer 1

`Total = 32.4in^2`

Explanation:

Given

See attachment for triangle

Required

The surface area of the pyramid

To do this, we calculate the surface area of each of the pyramid faces.

For the equilateral triangle.

`Base = 4.5in`

`Height = 3.9in`

The area is:

`A_1 = 0.5 * Base * Height`

`A_1 = 0.5 * 4.5in * 3.9in`

`A_1 = 8.775in^2`

There are 3 isosceles triangles of equal dimension.

`Base = 4.5in`

`Height = 3.5in`

The area of one of them is:

`A_2 = 0.5 * 4.5in * 3.5in`

`A_2 = 7.875in^2`

For the 3, the surface area is:

`3A_2 = 7.875in^2 * 3`

`3A_2 = 23.625in^2\\`

The total surface area is:

`Total = 8.775in^2 + 23.625in^2`

`Total = 32.4in^2`