Question

what is the surface area of this triangular prism? 17 in. 8 in. 17 in. 30 in. 9 in. square inches

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 9$ in and $h = 8$ in. So, $A_{triangle}=\frac{1}{2}\times9\times8=36$ square - inches. Since there are 2 triangular faces, the total area of triangular faces is $2\times36 = 72$ square - inches.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 17 in (length) and 9 in (width). So, $A_{rect1}=17\times9 = 153$ square - inches.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 17 in (length) and 17 in (width). So, $A_{rect2}=17\times17 = 289$ square - inches.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 17 in (length) and 30 in (width). So, $A_{rect3}=17\times30 = 510$ 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 and rectangular faces. $A=72 + 153+289+510=1024$ square - inches.

Answer:

1024