Question

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 centimeters long, and the height of the equilateral triangle is 3.5 centimeters. The pyramid's slant height is 8 centimeters. What is its surface area?

Answer 1

The surface area is 55 cm².

Explanation:

The formula to compute the surface area of the triangular pyramid is:

`SA=(0.50* \text{Base Perimeter}* h)+\text{Base Area}`

Here h is the slant height.

Compute the Base perimeter as follows:

Perimeter of the equilateral triangle = 3 × side

= 3 × 4

= 12 cm

Compute the Base area as follows:

Area of the equilateral triangle = 0.50 × side × height

= 0.50 × 4 × 3.50

= 7 cm²

Compute the surface area as follows:

`SA=(0.50* \text{Base Perimeter}* h)+\text{Base Area}`

`=(0.50* 12* 8)+7\\=48+7\\=55\ \text{cm}^(2)`

Thus, the surface area is 55 cm².