Question

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

Explanation:

Step1: Calculate area of triangular bases

The area of a triangle formula is $A=\frac{1}{2}bh$. For the triangular bases with $b = 24$ yd and $h=18$ yd, $A_{base}=\frac{1}{2}\times24\times18= 216$ yd². Since there are 2 bases, the total area of bases is $2\times216 = 432$ yd².

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions 24 yd and 30 yd. So its area $A_1=24\times30 = 720$ yd².

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions 18 yd and 30 yd. So its area $A_2=18\times30=540$ yd².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 25 yd and 30 yd. So its area $A_3=25\times30 = 750$ yd².

Step5: Calculate total surface area

The total surface area $A = 432+720 + 540+750=2442$ yd².

Answer:

2442 yd²