Question

What is the total surface area of the prism shown below

Answer 1

The prism has 6 faces.
Each pair of opposite faces is congruent.

The front and back faces are rectangles that measure 10 cm by 5 cm.
The right and left faces are rectangles that measure 5 cm by 3 cm.
The top and bottom faces are rectangles that measure 10 cm by 3 cm.

Now we find the area of each rectangle.

The front and back faces are rectangles that measure 10 cm by 5 cm.
Each face:
A = 10 cm * 5 cm + 50 cm^2

The right and left faces are rectangles that measure 5 cm by 3 cm.
Each face:
A = 5 cm * 3 cm = 15 cm^2

The top and bottom faces are rectangles that measure 10 cm by 3 cm.
Each face:
A = 10 cm * 3 cm = 30 cm^2

There are two faces shaped like each rectangle above, so we multiply each rectangle's area by 2, and we add them together.

total surface area = 2 * 50 cm^2 + 2 * 15 cm^2 + 2 * 30 cm^2

total surface area = 100 cm^2 + 30 cm^2 + 60 cm^2

total surface area = 190 cm^2