Question

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 feet long, and the height of the equilateral triangle is 3.5 feet. The pyramid's slant height is 3 feet. What is the surface area?

Answer 1

Total surface area of the pyramid =
`25ft^(2)`

Explanation:

To find the surface area of the triangular- based pyramid, we will use the formula:

Surface area = Area of base + Area of the three faces

Area of base of the pyramid = Area of equilateral triangle =
`0.5 * base * height`

`= 0.5 * 4 * 3.5= 7ft ^(2)`

Area of the slant faces of the pyramid is
`0.5 * base * slant height`

`0.5 * 4 * 3 = 6 ft^(2)`

Since there are 3 slant surfaces the total surface area of the pyramid =
`7 + 3 * (6)= 25ft^(2)`