Question

find the surface area of the triangular prism shown below. units²

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A_{triangle}=\frac{1}{2}bh$. Here, $b = 5$ and $h=4$, so $A_{triangle}=\frac{1}{2}\times5\times4 = 10$.

Step2: Calculate area of rectangular faces

There are three rectangular faces.

• For the face with dimensions 5 and 7: $A_1 = 5\times7=35$.
• For the face with dimensions 6 and 7: $A_2 = 6\times7 = 42$.
• For the face with dimensions 5 and 7: $A_3=5\times7 = 35$.

Step3: Calculate total surface - area

The total surface area $A$ of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces. $A=2\times A_{triangle}+A_1 + A_2+A_3$. Substitute the values: $A = 2\times10+35 + 42+35=142$.

Answer:

142