How do you find the surface area of a triangular prism.
SA = 2B + Ph
SA = 2(1/2ab) + (b + c + d)h
SA = ab + (b + c + d)h
twice the area of the triangle at the base (to include the top) plus the height times the sum of the lengths of the triangle legs (to include the three rectangular sides).
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HI
To find the surface area of a triangular prism, you need to calculate the sum of the areas of all its faces. A triangular prism has three rectangular faces (two triangular bases and three rectangular lateral faces).
To calculate the surface area, follow these steps:
1. Calculate the area of the triangular bases:
- Measure the length of the base (b) and the height (h) of one of the triangular bases.
- Use the formula for the area of a triangle: Area = 0.5 * b * h.
- Multiply the area by 2 since there are two triangular bases.
2. Calculate the area of the rectangular lateral faces:
- Measure the length (l) of one of the three rectangular lateral faces.
- Measure the height (h) of the triangular base.
- Multiply the length, height, and the number of rectangular lateral faces (3).
- The formula for the area of a rectangle is: Area = l * h.
3. Add the areas of the triangular bases and the rectangular lateral faces to find the total surface area.
Let's go through an example:
Suppose the length of the base of one of the triangular bases is 6 cm, and the height is 4 cm. The length of one of the rectangular lateral faces is 10 cm.
1. Area of triangular bases:
Area = 0.5 * 6 cm * 4 cm = 12 cm^2
Total area of the two bases: 2 * 12 cm^2 = 24 cm^2
2. Area of rectangular lateral faces:
Area = 10 cm * 4 cm = 40 cm^2
Total area of three faces: 3 * 40 cm^2 = 120 cm^2
3. Total surface area: 24 cm^2 + 120 cm^2 = 144 cm^2
Therefore, the surface area of the triangular prism is 144 square centimeters.