Question

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 20 inches long, and the height of the equilateral triangle is 17.3 inches. The pyramid's slant height is 13 inches. What is its surface area?

Answer 1

Answer:

Surface area of pyramid with base equilateral triangle is $390+100\sqrt{3}$ square inches

Step-by-step explanation:

Recall the following result:

The total surface area(S) of a regular pyramid is given by,

$S = \frac{1}{2}pl+B$                                       ...... (1)

Here, p represents the perimeter of the base , $l$ the slant height and B the base area of the pyramid.

From the given information:

Side of equilateral triangle = 20 inches

Slant height of the pyramid($l$) = 13 inches.

First find the perimeter and Area of the base pyramid.

Perimeter of equilateral triangle(p) = $3 \times (side)$

                                                          = $3 \times 20 = 60 inches$

Area of equilateral triangle(B) = $\frac{\sqrt{3} }{4} \times (side)^{2}$

                                                 =$\frac{\sqrt{3} }{4} \times (20)^2 = 100\sqrt{3}$  square inches.

Substitute the above values in equation (1) as shown below:

$S=\frac{1}{2} \times 60 \times 13+100\sqrt{3}$

$S= 390+100\sqrt{3}$ square inches

Hence, the surface area of pyramid with base equilateral triangle is $390+100\sqrt{3}$ square inches.