Question

makayla is decorating the outside of a box in the shape of a triangular prism. t shows a net for the box. what is the surface area of the box, in square centimeters, that makayla decorates?

Explanation:

Step1: Calculate the area of the two triangular faces

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 7\) cm and \(h=9\) cm.

$$A_{triangle}=\frac{1}{2}\times7\times9 = 31.5\space cm^{2}$$

Since there are two triangular faces, \(A_{total - triangles}=2\times31.5 = 63\space cm^{2}\)

Step2: Calculate the area of the three rectangular faces

• For the rectangle with dimensions \(12\times7\): \(A_{1}=12\times7 = 84\space cm^{2}\)
• For the rectangle with dimensions \(12\times11.4\): \(A_{2}=12\times11.4=136.8\space cm^{2}\)
• For the rectangle with dimensions \(12\times11.4\) (the other congruent non - base rectangle): \(A_{3}=12\times11.4 = 136.8\space cm^{2}\)

Step3: Calculate the total surface area

$$A_{total}=A_{total - triangles}+A_{1}+A_{2}+A_{3}$$

$$A_{total}=63 + 84+136.8+136.8$$

$$A_{total}=420.6\space cm^{2}$$

Answer:

\(420.6\space cm^{2}\)