Question

Find the surface area of the square pyramid (above) using its net (below)

Answer 1

33 units²

Explanation:

Use the formula for the surface area of a square pyramid:

`S.A.=b^2+2bh`

Where b is the base, and h is the slant height.

Substitute:

`S.A.=3^2+2(3)(4)\\S.A.=9+24\\S.A.=33`

Or use the net and solve for the area of each shape:

Area of square:

`A_s=3^2\\A_s=9`

Area of 4 triangles:

`A_t=(bh)/(2)\\A_t=((3)(4))/(2)\\A_t=(12)/(2)\\A_t=6\\4A_t=(4)(6)\\4A_t=24`

Add both results up:

`S.A.=24+9\\S.A.=33`

And put units² at the end.