Question

what is the surface area of this triangular prism? 25 in. 15 in. 25 in. 40 in. 9 in. square inches

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 40$ in and $h=15$ in. So, $A_{base}=\frac{1}{2}\times40\times15= 300$ square - inches. Since there are 2 triangular bases, the total area of the bases is $2\times300 = 600$ square - inches.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1: With dimensions 9 in and 40 in, $A_1=9\times40 = 360$ square - inches.
Face 2: With dimensions 9 in and 25 in, $A_2=9\times25 = 225$ square - inches.
Face 3: With dimensions 9 in and 25 in, $A_3=9\times25 = 225$ square - inches.
The total area of the rectangular faces is $A_{rect}=360 + 225+225=810$ square - inches.

Step3: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the area of the bases and the area of the rectangular faces. So, $A = 600+810=1410$ square - inches.

Answer:

1410