Question

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find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Find area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. For the triangular bases with $b = 15$ yd and $h=20$ yd, $A_{base}=\frac{1}{2}\times15\times20 = 150$ yd². Since there are 2 bases, the total area of the bases is $2\times150=300$ yd².

Step2: Find area of rectangular faces

There are 3 rectangular faces.

• First face with dimensions 17 yd (height of prism) and 15 yd: $A_1 = 17\times15=255$ yd².
• Second face with dimensions 17 yd and 20 yd: $A_2=17\times20 = 340$ yd².
• Third face with dimensions 17 yd and 25 yd: $A_3=17\times25=425$ yd².

The total area of the rectangular faces is $A_{rect}=255 + 340+425=1020$ yd².

Step3: Calculate total surface - area

The surface - area of the triangular prism $A = A_{base}+A_{rect}$. So $A=300 + 1020=1320$ yd².

Answer:

1320 yd²