What is the surface area of the triangular prism?

Full solution

Q. What is the surface area of the triangular prism?

Identify Faces of Prism: Identify the faces of the prism: two triangular bases and three rectangular sides.
Calculate Triangular Base Area: Calculate the area of one triangular base. Assume base $b$ and height $h$ are given: $\text{Area} = \frac{1}{2} \times b \times h$ .
Double Triangular Base Area: Double the area of the triangular base to account for both ends of the prism: Total area of triangular bases = $2 \times \left(\frac{1}{2} \times b \times h\right)$ .
Calculate Rectangular Sides Area: Calculate the area of the three rectangular sides. Assume lengths $l_1$ , $l_2$ , and $l_3$ are given: Total area of rectangular sides = $l_1 \times h + l_2 \times h + l_3 \times h$ .
Find Total Surface Area: Add the areas of the bases and the rectangular sides to find the total surface area: Surface Area = $2 \times \left(\frac{1}{2} \times b \times h\right) + l_1 \times h + l_2 \times h + l_3 \times h$ .
Simplify Equation: Simplify the equation: $\text{Surface Area} = b \times h + l_1 \times h + l_2 \times h + l_3 \times h$ .
Calculate Surface Area: Plug in the given values for $b$ , $h$ , $l_1$ , $l_2$ , and $l_3$ to calculate the surface area.