Question

This net can be folded to make a square pyramid. What is the surface area of the pyramid?

Answer 1

Answer:  

$85in^2$

Step-by-step explanation:

to find the surface area we need to find the followng areas:  

• area of the square  

• area of a triangle and multiply it by 4 (because there are 4 triangles)

And once we have those areas, we add them to find the surface area.

Area of the square:

the formula to find the area of a square is:

$a_{square}=l^2$

where $l$ is the length of the side: $l=5in$

thus the area of the square is:

$a_{square}=(5in)^2\\a_{square}=25in^2$

Area of the triangles:

the are of 1 triangle is given by

$a_{triangle}=\frac{b*h}{2}$

where $b$ is the base of the triangle: $b=5in$ (the base of the triangle is the side of the square)

and $h$ is the height of the triangle: $h=6in$

thus, the area of 1 triangle is:

$a_{triangle}=\frac{(5in)*(6in)}{2}\\ a_{triangle}=\frac{30in^2}{2}\\ a_{triangle}=15in^2$

the area of the 4 triangles is (we multiply by 4):

$a_{4-triangles}=4(15in^2)\\a_{4-triangles}=60in^2$

finally we add the area of the square and the area of the 4 triangles to find the total surface area:

$Surface=25in^2+60in^2\\Surface=85in^2$