Question

roxy is doing an origami project. she is building the pyramid shown in the drawing. she needs 1 sheet of origami paper for every 2 square centimeters of surface area. how many sheets of paper does she need? you may select the formula needed to solve this problem from the formula sheet. click on the formula sheet icon to open it. select one: a. 36 b. 42 c. 48 d. 84

Explanation:

Step1: Calculate base area

The base is a square with side - length $a = 6$ cm. The area of the base $B=a^{2}=6^{2}=36$ $cm^{2}$.

Step2: Calculate area of one triangular face

The base of each triangular face is $b = 6$ cm and the height is $h = 4$ cm. The area of a triangle is $A_{\triangle}=\frac{1}{2}bh=\frac{1}{2}\times6\times4 = 12$ $cm^{2}$.

Step3: Calculate total surface area

The pyramid has 4 triangular faces and 1 square base. The total surface area $S=B + 4A_{\triangle}=36+4\times12=36 + 48=84$ $cm^{2}$.

Step4: Calculate number of paper sheets

She needs 1 sheet for every 2 square - centimeters of surface area. So the number of sheets $n=\frac{S}{2}=\frac{84}{2}=42$.

Answer:

B. 42