Surface Area of a Right Triangular Prism
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A right triangular prism and its net are shown below. (All lengths are in yards.) (a) Find the following side lengths for the net. A = [] yd, B = [] yd, C = [] yd, D = [] yd. (b) Use the net to find the surface area of the prism. [] yd^2
This question includes visual content: The image shows a right triangular prism on the left and its corresponding net on the right. The prism has a triangular base with legs of 8 and 15, and a hypotenuse of 17. The height of the prism is 2. The net consists of three rectangles and two triangles. Several segments in the net are labeled with variables: A represents the height of the prism (between two rectangle sides), B represents the top edge of the central rectangular strip, C represents one of the legs of the triangular side in the net, and D represents the length of the central rectangular strip.
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Hi Peter, let's look at this right triangular prism and its net to find the missing side lengths and then calculate the total surface area.
Surface Area of a Triangular Prism
First, let's identify the dimensions of the prism. The triangular base is a right triangle with legs of fifteen and eight yards, and a hypotenuse of seventeen yards. The height or length of the prism is two yards.
Prism Dimensions
Now, let's map these to the net. Dimension A is the height of the rectangular panels, which corresponds to the height of the prism. So, A equals two yards.
Dimension B is the length of one leg of the triangular base. Looking at the diagram, B corresponds to the longer leg, so B is fifteen yards.
Dimension C is another side of the triangular base. It is the shorter leg, so C is eight yards.
Finally, dimension D is the width of the leftmost rectangular panel, which wraps around to match the hypotenuse of the triangle. Therefore, D is seventeen yards.
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