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. The triangular pyramid needs square inches of construction paper to make. The square pyramid needs square inches of construction paper to make. The pyramid will need square inches more construction paper to make than the other pyramid.

Answer 1

Answer:

A. 108 in^2

B. 144 in^2

C. 36 in^2

Step-by-step explanation:

Assuming that the pyramids are like the figure I attach.

It would be as follows:

Triangular pyramid:

It would be 4 times the area of ​​the triangle, since we assume that they are equal. We know that the height is 9 inches and that the base is 6 inches.

The area of ​​the triangle is the multiplication of the base times the height divided by two. So:

At = b * h / 2

At = 6 * 9/2

At = 27

27 square inches would be the area of ​​a single triangle, but since they are 4 it would be 4 * 27 = 108 square inches.

For a triangular-based pyramid it would take 108 square inches of paper.

Quadratic pyramid:

It would be 4 times the area of ​​the triangle, since we assume that they are equal and adding the base of the pyramid that would be the area of ​​a square. The area of ​​the square is equal to the base times the base or base to the square.

In other words, the total area calculated above would be 108 square inches adding the area of ​​the square. So

As = b * b

Ace = 6 * 6

Ace = 36

Therefore the final area would be 108 + 36 = 144 square inches.

For a square-based pyramid it would take 144 square inches of paper.

The difference between one and the other is 36 square inches, which is equivalent to the square base of the square pyramid.