Margo is creating a pencil caddy in the shape of a triangle prism. She is determining how much wood she needs to build the caddy. Her design is shown below
To calculate the amount of wood needed, Margo needs to find the surface area of the triangle prism.
The formula to find the surface area of a triangle prism is:
Surface Area = 2 * Base Area + (Perimeter of Base) * Height
In Margo's case, the triangle prism has a triangular base, so she needs to find the area and perimeter of the base triangle first.
Let's say the base triangle has a base of 4 inches and a height of 3 inches. Then, the area of the base triangle would be:
Base Area = (1/2) * Base * Height
Base Area = (1/2) * 4 * 3
Base Area = 6 square inches
Next, she needs to find the perimeter of the base triangle. Since it is an equilateral triangle with all sides measuring 4 inches, the perimeter would be:
Perimeter of Base = 3 * Side
Perimeter of Base = 3 * 4
Perimeter of Base = 12 inches
Now, Margo can plug these values into the formula for the surface area of the triangle prism:
Surface Area = 2 * Base Area + (Perimeter of Base) * Height
Surface Area = 2 * 6 + 12 * Height
Assuming the height of the prism is 5 inches, Margo can find the total surface area of the prism:
Surface Area = 2 * 6 + 12 * 5
Surface Area = 12 + 60
Surface Area = 72 square inches
Therefore, Margo would need 72 square inches of wood to build the pencil caddy in the shape of a triangle prism.