Question

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

Answer 1

`85in^2`

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) =(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) =((5in)*(6in))/(2)`

`a_(triangle) =(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`