Difference between revisions of "Find Surface Area of a Triangular Prism"
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| − | A prism is a three-dimensional shape with two parallel, congruent bases.<ref>http://www.mathopenref.com/prism.html</ref> In a triangular prism, the bases are triangles. A triangular prism also has three lateral sides. To find the surface area of triangular prism, you first need to find the area of the lateral sides, then you need to find the area of the bases. Finally, you need to add these two areas together to find the total surface area. These steps are represented by the formula <math>\text{surface area} = L + 2B</math>, where <math>L</math> equals the lateral area of the prism and <math>B</math> equals the area of one base. | + | A prism is a three-dimensional shape with two parallel, congruent bases.<ref name="rf1">http://www.mathopenref.com/prism.html</ref> In a triangular prism, the bases are triangles. A triangular prism also has three lateral sides. To find the surface area of triangular prism, you first need to find the area of the lateral sides, then you need to find the area of the bases. Finally, you need to add these two areas together to find the total surface area. These steps are represented by the formula <math>\text{surface area} = L + 2B</math>, where <math>L</math> equals the lateral area of the prism and <math>B</math> equals the area of one base. |
[[Category:Calculating Volume and Area]] | [[Category:Calculating Volume and Area]] | ||
==Steps== | ==Steps== | ||
===Finding the Lateral Area=== | ===Finding the Lateral Area=== | ||
| − | #Write down the formula for finding the lateral area of a triangular prism. The formula is <math>L = Ph</math>, where <math>L</math> equals the lateral area of the prism, <math>P</math> equals the perimeter of one base, and <math>h</math> equals the height of the prism.<ref>http://www.virtualnerd.com/geometry/surface-area-volume-solid/prisms-cylinders-area/triangular-prism-lateral-surface-areas</ref> | + | #Write down the formula for finding the lateral area of a triangular prism. The formula is <math>L = Ph</math>, where <math>L</math> equals the lateral area of the prism, <math>P</math> equals the perimeter of one base, and <math>h</math> equals the height of the prism.<ref name="rf2">http://www.virtualnerd.com/geometry/surface-area-volume-solid/prisms-cylinders-area/triangular-prism-lateral-surface-areas</ref> |
| − | #*The lateral area of a prism is the surface area of all sides, or faces, that are not the base.<ref>http://mathcentral.uregina.ca/qq/database/qq.09.06/s/crystal1.html</ref> | + | #*The lateral area of a prism is the surface area of all sides, or faces, that are not the base.<ref name="rf3">http://mathcentral.uregina.ca/qq/database/qq.09.06/s/crystal1.html</ref> |
| − | #Calculate the perimeter of one base. The base is a triangle, so it will have three sides. The area of the perimeter of a triangle is <math>\text{Perimeter} = a + b + c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are the length of each side of the triangle.<ref>http://www.mathopenref.com/triangleperimeter.html</ref> It doesn’t matter which base you use to calculate, because the two bases of a prism are congruent.<ref>http://www.regentsprep.org/regents/math/geometry/gg2/PrismPage.htm</ref> | + | #Calculate the perimeter of one base. The base is a triangle, so it will have three sides. The area of the perimeter of a triangle is <math>\text{Perimeter} = a + b + c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are the length of each side of the triangle.<ref name="rf4">http://www.mathopenref.com/triangleperimeter.html</ref> It doesn’t matter which base you use to calculate, because the two bases of a prism are congruent.<ref name="rf5">http://www.regentsprep.org/regents/math/geometry/gg2/PrismPage.htm</ref> |
#*For example, if the base has three sides measuring 6 cm, 5 cm, and 4 cm, to calculate the perimeter, you would add up all three sides: <math>6 + 5 + 4 = 15</math>. So, the perimeter of one base is 15 cm. | #*For example, if the base has three sides measuring 6 cm, 5 cm, and 4 cm, to calculate the perimeter, you would add up all three sides: <math>6 + 5 + 4 = 15</math>. So, the perimeter of one base is 15 cm. | ||
#Plug the perimeter into the lateral area formula. Make sure you substitute for the variable <math>P</math> in the formula. | #Plug the perimeter into the lateral area formula. Make sure you substitute for the variable <math>P</math> in the formula. | ||
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===Finding the Area of the Base=== | ===Finding the Area of the Base=== | ||
| − | #Set up the formula for the area of a triangle. Since the bases of a triangular prism are triangles, you will use this formula to calculate their area. The formula for the area of a triangle is <math>A = \frac{1}{2}bh</math>, where <math>A</math> equals the area of the triangle, <math>b</math> equals the base of the triangle, and <math>h</math> equals the height of the triangle.<ref>http://www.mathwarehouse.com/geometry/triangles/area/index.php</ref> | + | #Set up the formula for the area of a triangle. Since the bases of a triangular prism are triangles, you will use this formula to calculate their area. The formula for the area of a triangle is <math>A = \frac{1}{2}bh</math>, where <math>A</math> equals the area of the triangle, <math>b</math> equals the base of the triangle, and <math>h</math> equals the height of the triangle.<ref name="rf6">http://www.mathwarehouse.com/geometry/triangles/area/index.php</ref> |
#*This is the most common way to calculate the area of a triangle. If you don’t know the height of the triangle, you can also [[Calculate the Area of a Triangle | calculate the area]] using the length of the triangle’s three sides. | #*This is the most common way to calculate the area of a triangle. If you don’t know the height of the triangle, you can also [[Calculate the Area of a Triangle | calculate the area]] using the length of the triangle’s three sides. | ||
| − | #*You only need to find the area of one base, since the two bases of a prism are congruent, and will therefore have the same area.<ref | + | #*You only need to find the area of one base, since the two bases of a prism are congruent, and will therefore have the same area.<ref name="rf5" /> |
#Plug the base of the triangle into the formula. Don’t confuse the base for another side of the triangle. The base is the side perpendicular to the height. | #Plug the base of the triangle into the formula. Don’t confuse the base for another side of the triangle. The base is the side perpendicular to the height. | ||
#*For example, if the base of the triangle is 6 cm, your formula will look like this: <math>A = \frac{1}{2}6h</math>. | #*For example, if the base of the triangle is 6 cm, your formula will look like this: <math>A = \frac{1}{2}6h</math>. | ||
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===Finding the Surface Area=== | ===Finding the Surface Area=== | ||
| − | #Set up the formula for finding the surface area of a prism. The formula is <math>SA = L + 2B</math>, where <math>SA</math> equals the surface area of the prism, <math>L</math> equals the lateral area of the prism, and <math>B</math> equals the area of one base.<ref>https://www.andrews.edu/~calkins/math/webtexts/geom10.htm</ref> | + | #Set up the formula for finding the surface area of a prism. The formula is <math>SA = L + 2B</math>, where <math>SA</math> equals the surface area of the prism, <math>L</math> equals the lateral area of the prism, and <math>B</math> equals the area of one base.<ref name="rf7">https://www.andrews.edu/~calkins/math/webtexts/geom10.htm</ref> |
#Plug the lateral area into the formula. This is the surface area of all sides of the prism that are not the base. You should have calculated this previously. Make sure that you substitute the lateral area for the variable <math>L</math>. | #Plug the lateral area into the formula. This is the surface area of all sides of the prism that are not the base. You should have calculated this previously. Make sure that you substitute the lateral area for the variable <math>L</math>. | ||
#*For example, if the lateral area of your triangular prism is 135 square centimeters, your formula will look like this: <math>SA = 135 + 2B</math>. | #*For example, if the lateral area of your triangular prism is 135 square centimeters, your formula will look like this: <math>SA = 135 + 2B</math>. | ||
