What is the total surface area of the triangular prism in square centimeters?

Steps to Solve

1. Calculate the area of the two triangles

The area of one triangle is given by:

$Area = \frac{1}{2} \times base \times height = \frac{1}{2} \times 12 \times 8 = 48 \ m^2$.

Since there are two triangles, their combined area is $2 \times 48 = 96 \ m^2$.

2. Calculate the area of the three rectangles

The areas of the three rectangles are:

Rectangle 1: $20 \times 10 = 200 \ m^2$

Rectangle 2: $20 \times 10 = 200 \ m^2$

Rectangle 3: $20 \times 12 = 240 \ m^2$

The combined area of the three rectangles is $200 + 200 + 240 = 640 \ m^2$.

3. Calculate the total surface area in square meters

The total surface area of the triangular prism is the sum of the areas of the two triangles and the three rectangles:

$96 + 640 = 736 \ m^2$.

4. Convert the surface area from square meters to square centimeters

Since $1 \ m = 100 \ cm$, then $1 \ m^2 = (100 \ cm)^2 = 10000 \ cm^2$. Therefore we have $736 \ m^2 = 736 \times 10000 \ cm^2 = 7360000 \ cm^2$.