Question

Karina is creating two pyramids with the nets below using construction paper. In both nets, all of the triangular faces of the pyramids have a height of 9 inches and a base of 6 inches. Compare the amount of construction paper needed to make each pyramid.

Answer 1

144 sq in

Explanation:

Face height=9, bases=6 in

#Assume the pyramid has a square base.

First we need to calculate the perpendicular height of the pyramid:

`#Pythagorean \ Theorem\\a^2+b^2=c^2\\9^2-(0.5* 6)^2=h^2\\72=h^2\\h=√(72) \ in`

Now to find the surface area of each pyramid:

`A=lw+l√((w/2)^2+h^2)+w√((l/w)^2+h^2)\\\\\#w=l=6,h=√(72)\\\\A=6^2+6√((6/2)^2+72)+6√((6/6)^2+72)\\\\A\approx 144\ sq \ in`

Hence amount of construction paper needed to make each pyramid is 144 sq in