Question

what is the surface area of the triangular prism? square inches

Explanation:

Step1: Calculate area of triangular faces

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 20$ in and $h=15$ in. So, $A_{triangle}=\frac{1}{2}\times20\times15= 150$ square - inches. Since there are 2 triangular faces, the total area of triangular faces is $2\times150 = 300$ square - inches.

Step2: Calculate area of first rectangular face

The dimensions of the first rectangular face are $l = 30$ in and $w = 20$ in. So, $A_{rect1}=30\times20 = 600$ square - inches.

Step3: Calculate area of second rectangular face

The dimensions of the second rectangular face are $l = 30$ in and $w = 25$ in. So, $A_{rect2}=30\times25 = 750$ square - inches.

Step4: Calculate area of third rectangular face

The dimensions of the third rectangular face are $l = 30$ in and $w = 20$ in. So, $A_{rect3}=30\times20 = 600$ square - inches.

Step5: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $A=300 + 600+750 + 600=2250$ square - inches.

Answer:

2250