Question

find the surface area of the triangular prism shown below.

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. For the triangular bases with base $b = 6$ and height $h=4$, we have $A_{base}=\frac{1}{2}\times6\times4= 12$. Since there are 2 triangular bases, the total area of the bases is $2\times12 = 24$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.

• For the face with dimensions $5\times7$, its area $A_1=5\times7 = 35$.
• For the face with dimensions $5\times7$, its area $A_2=5\times7=35$.
• For the face with dimensions $6\times7$, its area $A_3=6\times7 = 42$.

The total area of the rectangular faces is $A_{rect}=35 + 35+42=112$.

Step3: Calculate total surface - area

The surface area $S$ of the triangular prism is the sum of the area of the bases and the area of the rectangular faces. So $S=24 + 112=136$.

Answer:

136