Question

what is the surface area of this triangular prism? 20 in. 25 in. 30 in. 15 in. square inches

Explanation:

Step1: Calculate area of triangular faces

The triangular faces have base $b = 15$ in and height $h = 20$ in. Area of a triangle $A_{triangle}=\frac{1}{2}bh$. So $A_{triangle}=\frac{1}{2}\times15\times20 = 150$ square - inches. Since there are 2 triangular faces, the total area of triangular faces $A_{t}=2\times150 = 300$ square - inches.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions $l = 25$ in and $w = 15$ in. Area of a rectangle $A_{1}=25\times15=375$ square - inches.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions $l = 25$ in and $w = 20$ in. Area of a rectangle $A_{2}=25\times20 = 500$ square - inches.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $l = 25$ in and $w = 30$ in. Area of a rectangle $A_{3}=25\times30=750$ 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 faces and the rectangular faces. $A=A_{t}+A_{1}+A_{2}+A_{3}=300 + 375+500+750=1925$ square - inches.

Answer:

1925