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How to calculate surface area of a right triangular prism?
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The total surface area of a triangular prism is the sum of the areas of all its faces: the three lateral faces (rectangles) and two bases (triangles). The most general formula for the surface area of any prism is: Total area = Lateral area + 2 × Base area.
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The surface area of a right triangular prism can be calculated by representing the 3-d figure into a 2-d net, which makes it easier to understand.
In order to calculate the surface area of a triangular prism: Calculate the area of each face. Add the five areas together. Include the units. Surface area of a triangular prism examples. Example 1: how to find the surface area of a right triangular prism. Calculate the surface area of the triangular prism. Calculate the area of each face.
- Overview
- Finding the Lateral Area
- Finding the Area of the Base
- Finding the Surface Area
A prism is a three-dimensional shape with two parallel, congruent bases.
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 , where equals the lateral area of the prism and equals the area of one base.
Write down the formula for finding the lateral area of a triangular prism.
The formula is , where equals the lateral area of the prism, equals the perimeter of one base, and equals the height of the prism.
The lateral area of a prism is the surface area of all sides, or faces, that are not the base.
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 , where , , and are the length of each side of the triangle.
It doesn’t matter which base you use to calculate, because the two bases of a prism are congruent.
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 , where equals the area of the triangle, equals the base of the triangle, and equals the height of the triangle.
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
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.
Plug the base of the triangle into the formula.
Set up the formula for finding the surface area of a prism.
The formula is , where equals the surface area of the prism, equals the lateral area of the prism, and equals the area of one base.
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 .
For example, if the lateral area of your triangular prism is 135 square centimeters, your formula will look like this:
Plug the area of one base into the formula.
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Jul 24, 2020 · Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with triangular prism surface area. Mr. J will go through calculating...
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Jul 29, 2024 · Usually, what you need to calculate are the triangular prism volume and its surface area. The two most basic equations are: volume = 0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area), where a, b, c are sides of the ...
Aug 3, 2023 · The surface area of a triangular prism is the entire space occupied by its outermost layers (or faces). It is expressed in square units such as m 2, cm 2, mm 2, and in 2. Formulas. Like all 3-dimensional shapes, 2 types of surface areas can be calculated for a triangular prism. Lateral Surface Area
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