Respuesta :
Answer:
Surface area of pyramid with base equilateral triangle is [tex]390+100\sqrt{3}[/tex] square inches
Step-by-step explanation:
Recall the following result:
The total surface area(S) of a regular pyramid is given by,
[tex]S = \frac{1}{2}pl+B[/tex] ...... (1)
Here, p represents the perimeter of the base , [tex]l[/tex] 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([tex]l[/tex]) = 13 inches.
First find the perimeter and Area of the base pyramid.
Perimeter of equilateral triangle(p) = [tex]3 \times (side)[/tex]
= [tex]3 \times 20 = 60 inches[/tex]
Area of equilateral triangle(B) = [tex]\frac{\sqrt{3} }{4} \times (side)^{2}[/tex]
=[tex]\frac{\sqrt{3} }{4} \times (20)^2 = 100\sqrt{3}[/tex] square inches.
Substitute the above values in equation (1) as shown below:
[tex]S=\frac{1}{2} \times 60 \times 13+100\sqrt{3}[/tex]
[tex]S= 390+100\sqrt{3}[/tex] square inches
Hence, the surface area of pyramid with base equilateral triangle is [tex]390+100\sqrt{3}[/tex] square inches.
