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

Question

asked Sep 23, 2021 225k views

2 Answers

Kaloyan · Answer 1 · 2021-09-29T12:27:12+0000

Answer:

85in^2

Explanation:

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

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

and
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:

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