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raketka [301]
3 years ago
14

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

Mathematics
1 answer:
Eddi Din [679]3 years ago
5 0

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

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