Question

kevin wraps a gift box in the shape of a triangular pyramid. the figure below shows a net for the gift box. if all the triangles are equilateral, how much wrapping paper did he use, in square inches? answer attempt 2 out of 3 ( a=square mathrm{in}^2 )

Explanation:

Step1: Calculate the area of one triangular face

The formula for the area of a triangle is \(A = \frac{1}{2}\times base\times height\). Here, the base \(b = 5\) inches and the height \(h=4.33\) inches.

$$A_{single}=\frac{1}{2}\times5\times4.33$$

$$A_{single}= 10.825\space in^{2}$$

Step2: Calculate the total surface area

Since a triangular pyramid (tetrahedron) has \(4\) triangular faces and all are congruent (because they are equilateral with same base and height), the total surface area \(A_{total}=4\times A_{single}\)

$$A_{total}=4\times10.825$$

$$A_{total}=43.3\space in^{2}$$

Answer:

\(43.3\)