Use the image to answer the question.
An illustration shows the unfolded version of a triangular prism.
A long horizontal rectangle is divided into three horizontal segments. The length of the first and third rectangles are labeled as 9 and the width as 1.5. The length of the second rectangle, drawn with dashed lines, is 10.8. Two triangles are adjoined on the top and bottom of the second rectangle. The perpendicular height of the triangle is drawn with a dotted line from the apex to the center of the base and is labeled as 7.2. It is marked by a right angle symbol.
Party Pizza Palace has cardboard containers for customers ordering only one slice of pizza to go. The container is made of cardboard and is in the shape of a triangular prism. The top and bottom are made of red cardboard, and the lateral faces are made of white cardboard. How much white cardboard is needed to make one pizza container?
(1 point)
in.2
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page 13 of 14
To find the amount of white cardboard needed to make one pizza container, we need to calculate the surface area of the lateral faces of the triangular prism.
The lateral faces of a triangular prism consist of three rectangles and two triangles. The rectangles are the sides of the prism, and the triangles are the top and bottom of the prism.
The formula to find the surface area of a triangular prism is:
Surface Area = 2(base perimeter) + (height × base perimeter)
In this case, the base perimeter is the sum of the three segments of the horizontal rectangle, so:
Base Perimeter = 9 + 10.8 + 9 = 28.8
The height of the prism is the perpendicular height of the triangle, which is 7.2.
Now, we can calculate the surface area of the lateral faces:
Surface Area = 2(28.8) + (7.2 × 28.8)
Surface Area = 57.6 + 207.36
Surface Area = 264.96 in.2
Therefore, 264.96 square inches of white cardboard are needed to make one pizza container.