Question

what is the surface area of this triangular prism? 12 in. 13 in. 8.5 in. 5 in. square inches

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces with $b = 5$ in and $h= 12$ in, $A_{triangle}=\frac{1}{2}\times5\times12 = 30$ square - inches. Since there are 2 triangular faces, the total area of triangular faces is $2\times30=60$ square - inches.

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions $12$ in (height) and $8.5$ in (width). So its area $A_{1}=12\times8.5 = 102$ square - inches.

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions $13$ in (slant - length) and $8.5$ in (width). So its area $A_{2}=13\times8.5 = 110.5$ square - inches.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $5$ in (base of triangle) and $8.5$ in (width). So its area $A_{3}=5\times8.5 = 42.5$ square - inches.

Step5: Calculate total surface area

The total surface area $A_{total}$ of the triangular prism is the sum of the areas of the two triangular faces and the three rectangular faces. $A_{total}=60 + 102+110.5 + 42.5=315$ square - inches.

Answer:

315