Question

rashaad is decorating the outside of a box in the shape of a triangular prism. the figure below shows a net for the box. what is the surface area of the box, in square centimeters, that rashaad decorates? answer attempt 1 out of 3 ( a=square mathrm{cm}^{2} )

Explanation:

Step1: Calculate the area of the two triangles

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is \(14\) cm and the height is \(5\) cm.
\(A_{triangle}=\frac{1}{2}\times14\times5 = 35\) \(cm^{2}\). Since there are two triangles, \(A_{total - triangles}=2\times35=70\) \(cm^{2}\)

Step2: Calculate the area of the three rectangles

• For the rectangle with sides \(14\) cm and \(13\) cm: \(A_{1}=14\times13 = 182\) \(cm^{2}\)
• For the two rectangles with sides \(13.93\) cm and \(14\) cm: \(A_{2}=2\times(13.93\times14)=2\times195.02 = 390.04\) \(cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(A = A_{total - triangles}+A_{1}+A_{2}\)
\(A=70 + 182+390.04\)
\(A = 642.04\) \(cm^{2}\)

Answer:

\(642.04\) \(cm^{2}\)