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How to Find the Surface Area of a Right Triangular Prism?Ī right triangular prism has two parallel and congruent triangular faces and three rectangular faces that are perpendicular to the triangular faces. Lateral Surface Area = (S 1 + S 2 + S 3) × l = (Perimeter × Length) or LSA = p × l Thus, the lateral surface area of triangular prism is: Observe the following figure to understand the lateral surface and the base of a triangular prism. The perimeter of the base is the total length of the edges of the base triangle, while the length of the prism is its height.
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The lateral surface area of a triangular prism can be calculated by multiplying the perimeter of the base by the length of the prism. When a triangular prism has its bases facing up and down, the lateral area is the area of the vertical faces. In other words, the lateral surface area of a triangular prism is calculated without considering the base area. The lateral surface area of any solid is the area without the bases. (bh) is the combined area of the two triangular faces = bh.S 1, S 2, and S 3 are the three edges (sides) of the base triangle.b is the bottom edge of the base triangle,.Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S 1 +S 2 + S 3)L + bh The formula for the surface area of triangular prism is: Observe the following figure of a triangular prism to know the dimensions that are considered to frame the formula. The triangular prism formula for surface area is formed by adding up the area of all the rectangular and triangular faces of a prism. All the other cases can be calculated with our triangular prism calculator.Formula for Surface Area of Triangular Prism The only case when we can't calculate triangular prism area is when the area of the triangular base and the length of the prism are given (do you know why? Think about it for a moment). Using law of sines, we can find the two sides of the triangular base:Īrea = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2)
![formula for triangular prism surface area formula for triangular prism surface area](https://i.pinimg.com/736x/22/69/de/2269de2f1cfc87fa2a9ab03f53621329--surface-area-the-surface.jpg)
Triangular base: given two angles and a side between them (ASA) Using law of cosines, we can find the third triangle side:Īrea = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle) Triangular base: given two sides and the angle between them (SAS) However, we don't always have the three sides given. area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area).
![formula for triangular prism surface area formula for triangular prism surface area](https://image4.slideserve.com/8157791/3-find-the-surface-area-of-the-triangular-prism-l.jpg)
If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base : You can calculate that using trigonometry: Length * Triangular base area given two angles and a side between them (ASA) You can calculate the area of a triangle easily from trigonometry: Length * Triangular base area given two sides and the angle between them (SAS) If you know the lengths of all sides, use the Heron's formula to find the area of the triangular base: Length * Triangular base area given three sides (SSS) It's this well-known formula mentioned before: Length * Triangular base area given the altitude of the triangle and the side upon which it is dropped Our triangular prism calculator has all of them implemented. A general formula is volume = length * base_area the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. In the triangular prism calculator, you can easily find out the volume of that solid.