13 cm
12 cm
9 cm
5 cm
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
a. 287 cm^2
b. 240 cm^2
c. 330 cm^2
d. 810 cm^2
To find the total surface area of the triangular prism, we add the area of all the faces.
Given:
Base: triangle with sides of 13 cm, 12 cm, and 5 cm
Height: 9 cm
The equation for the surface area of a triangular prism is:
Surface Area = area of two triangular bases + area of three rectangular sides
First, calculate the area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 13 * 9 = 58.5 cm^2 (for one base)
Area = 1/2 * 12 * 9 = 54 cm^2 (for the other base)
Total area for two triangular bases = 58.5 + 54 = 112.5 cm^2
Next, calculate the area of the three rectangular sides:
Rectangle 1: 13 cm (base) x 9 cm (height) = 117 cm^2
Rectangle 2: 12 cm (base) x 9 cm (height) = 108 cm^2
Rectangle 3: 5 cm (base) x 9 cm (height) = 45 cm^2
Total area for three rectangular sides = 117 + 108 + 45 = 270 cm^2
Finally, add the total area of the two triangular bases and three rectangular sides:
Total Surface Area = 112.5 + 270 = 382.5 cm^2
Therefore, the correct amount of plastic wrap needed to cover the wedge of cheese is estimated to be approximately 383 cm^2. None of the answer choices is exact but the closest is 330 cm^2 so the answer is c. 330 cm^2