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 total surface area of the pizza container, we first need to find the lateral surface area of the triangular prism.
The lateral surface area of a triangular prism is calculated by adding the areas of the three rectangles that form the sides of the prism.
The first and third rectangles have a length of 9 and a width of 1.5, so the area of each is 9 * 1.5 = 13.5 in^2.
The second rectangle has a length of 10.8 and a width of 1.5, so the area is 10.8 * 1.5 = 16.2 in^2.
Therefore, the total lateral surface area of the pizza container is 13.5 + 13.5 + 16.2 = 43.2 in^2.
Since the lateral faces of the prism are made of white cardboard, you would need 43.2 in^2 of white cardboard to make one pizza container.