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

Answer:

144 sq in

Step-by-step 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:

$#Pythagorean \ Theorem\\a^2+b^2=c^2\\9^2-(0.5\times 6)^2=h^2\\72=h^2\\h=\sqrt{72} \ in$

Now to find the surface area of each pyramid:

$A=lw+l\sqrt{(w/2)^2+h^2}+w\sqrt{(l/w)^2+h^2}\\\\\#w=l=6,h=\sqrt{72}\\\\A=6^2+6\sqrt{(6/2)^2+72}+6\sqrt{(6/6)^2+72}\\\\A\approx 144\ sq \ in$

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