Question

find the surface area of the right triangular prism (above) using its net (below).

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the given right - triangle with base $b = 3$ and height $h = 4$, the area of one triangular face is $A_{triangle}=\frac{1}{2}\times3\times4=6$. Since there are 2 triangular faces, the total area of triangular faces is $2\times6 = 12$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
For the rectangle with dimensions $3\times7$, its area $A_1=3\times7 = 21$.
For the rectangle with dimensions $4\times7$, its area $A_2=4\times7=28$.
For the rectangle with dimensions $5\times7$, its area $A_3=5\times7 = 35$.
The total area of rectangular faces is $A_{rectangles}=21 + 28+35=84$.

Step3: Calculate total surface area

The surface area $S$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So $S=12 + 84=96$.

Answer:

96