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 faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 8$ yd and $h=6$ yd. So, $A_{triangle}=\frac{1}{2}\times8\times6= 24$ yd². Since there are 2 triangular faces, the total area of triangular faces is $2\times24 = 48$ yd².

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 9 yd (length) and 10 yd (width). So, $A_{rect1}=9\times10 = 90$ yd².

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 6 yd (length) and 10 yd (width). So, $A_{rect2}=6\times10 = 60$ yd².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 8 yd (length) and 10 yd (width). So, $A_{rect3}=8\times10 = 80$ yd².

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. $A=48 + 90+60 + 80=278$ yd².

Answer:

278 yd²