Answer:
Surface area of pyramid with base equilateral triangle is
square inches
Step-by-step explanation:
Recall the following result:
The total surface area(S) of a regular pyramid is given by,
...... (1)
Here, p represents the perimeter of the base ,
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(
) = 13 inches.
First find the perimeter and Area of the base pyramid.
Perimeter of equilateral triangle(p) = ![3 \times (side)](https://tex.z-dn.net/?f=3%20%5Ctimes%20%28side%29)
= ![3 \times 20 = 60 inches](https://tex.z-dn.net/?f=3%20%5Ctimes%2020%20%3D%2060%20inches)
Area of equilateral triangle(B) = ![\frac{\sqrt{3} }{4} \times (side)^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%20%5Ctimes%20%28side%29%5E%7B2%7D)
=
square inches.
Substitute the above values in equation (1) as shown below:
![S=\frac{1}{2} \times 60 \times 13+100\sqrt{3}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2060%20%5Ctimes%2013%2B100%5Csqrt%7B3%7D)
square inches
Hence, the surface area of pyramid with base equilateral triangle is
square inches.