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Published byEarl Patrick Modified over 8 years ago

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Volume and Surface Area of a Triangular Prism

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A triangular prism is a three- sided polyhedron with two parallel triangular bases and three rectangular faces. It should not be confused with a pyramid.

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Step 1: Identify the base and height of one of the triangular bases. The triangular bases of the triangular prism will have the same dimensions, so it doesn't matter which triangle you use. Volume of a Triangular Prism

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Find the base and the height of the triangle by locating the length of one of the sides of the triangle as well as the length of a line perpendicular to that first line.

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Step 2: Multiply them. This is the first step to finding the area of the base, which is, in the case of the triangular prism, a triangle. So: 3 cm x 4 cm = 12 cm 2. Don't forget to state your answer in square units since you're working with area.

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Step 3: Divide the result by two. To finish finding the area of the triangular base, simply divide 12 cm 2 by 2. So, 12 cm 2 /2 = 6 cm 2

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Step 4: Multiply this number by the height of the shape. Let's say the height of the triangular prism, or the length of one of its sides, is 10 cm. So, just multiply 6 cm 2 x 10 cm to find the volume of the triangular prism. 6 cm 2 x 10 cm = 60 cm 3. Don't forget to state your answer in cubic units since you're working with volume.

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You have just followed the simple formula for finding the volume of a triangular prism: V = (Area of the triangular base) X length

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Now you try! Get a white board, marker and eraser. It’s time for Showdown!

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90 cm 3

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96 cm 3

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960 cm 3

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Surface Area of a Triangular Prism: Just find the area of the three rectangles and two triangles and add them together.

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Step 1: Find the area of the base triangle. 6(8)/2 = 24cm 2

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Step 2: The other base will have the same area so add them together or multiply by 2. 6(8)/2 = 24cm 2 24 + 24 = 48cm 2

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Step 3: Find the area of each rectangle. 15(10) = 150cm 2 15(6) = 90cm 2 15(8) = 120cm 2

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Step 4: Add the area of each rectangle to the sum of the triangular bases. 24 + 24 = 48cm 2 15(10) = 150cm 2 15(6) = 90cm 2 15(8) = 120cm 2 48 + 150 + 90 + 120 = 408 cm 2

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Now you try! Get a white board, marker and eraser. It’s time for Showdown!

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672 cm 2

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164 cm 2

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96 cm 2

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