Question

The net of the triangle prism is shown below. Each of the bases is shaped like a isosceles triangle. What is the total surface area of the triangular prism in square centimeters

Answer 1

Given:

Height, h = 4 cm

Base, = 6 cm

Length, L = 20 cm

To find the permieter of the base which is the is isosceles triangle, let's find the two equal sides using pythagorean theorem.

We have:

`\begin{gathered} c=\sqrt[]{3^2+4^2} \\ \\ c=\sqrt[]{9+16} \\ \\ c=\sqrt[]{25} \\ \\ c=5 \end{gathered}`

thus, perimeter of the base is:

P = 5 + 5 + 6 = 16 cm

Thus, we have:

TSA =

`\begin{gathered} TSA=((1)/(2)*6*4)+((1)/(2)*6*4)+(20*5)+(20*5)+(20*6) \\ \\ \text{TSA}=12+12+100+100+120 \\ \\ \text{TSA}=344cm^2 \end{gathered}`