Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer. 13 in 5 in 10 in 12 in

Explanation:

Step1: Calculate area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 12$ in and $h = 5$ in. So, $A_{triangle}=\frac{1}{2}\times12\times5= 30$ in². Since there are 2 triangular faces, the total area of triangular faces is $2\times30 = 60$ in².

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions 10 in (length) and 13 in (width). So, $A_{rect1}=10\times13 = 130$ in².

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions 10 in (length) and 12 in (width). So, $A_{rect2}=10\times12 = 120$ in².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 10 in (length) and 5 in (width). So, $A_{rect3}=10\times5 = 50$ in².

Step5: Calculate total surface - area

The total surface area of the triangular prism $A = A_{triangles}+A_{rect1}+A_{rect2}+A_{rect3}=60 + 130+120 + 50=360$ in².

Answer:

360 in²