Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
810 cm2
240 cm2
287 cm2 330 cm2
To find the surface area of the triangular prism (including the three rectangular faces and two triangular faces), we first calculate the area of the two triangular faces.
The formula for the area of a triangle is 1/2 * base * height.
For the triangular face with a base of 9 cm and height of 5 cm, the area is 1/2 * 9 * 5 = 22.5 cm2.
Since there are two triangular faces, the total area for both triangular faces is 22.5 * 2 = 45 cm2.
Next, we calculate the area of the three rectangular faces.
The formula for the area of a rectangle is length * width.
For the three rectangular faces:
1. 12 cm * 5 cm = 60 cm2
2. 12 cm * 9 cm = 108 cm2
3. 9 cm * 5 cm = 45 cm2
Adding up the areas of the three rectangular faces: 60 + 108 + 45 = 213 cm2.
To find the total surface area, we add the areas of the two triangular faces and the three rectangular faces:
45 cm2 (triangular faces) + 213 cm2 (rectangular faces) = 258 cm2.
Therefore, 258 cm2 of plastic wrap is needed to cover the wedge of cheese.
None of the provided answers match our calculation, so there seems to have been an error in the previous calculations or in the provided options.