surface area and volume of triangular prism

#Surface area and volume of triangular prism how to#

Step 3: Add all the areas together to get the total surface area of a right triangular prism in square units.

Step 2: Find the product of the length of the prism and the perimeter of the base triangle which will give the lateral surface area = (S 1 + S 2 + h) × l.

Step 1: Find the area of the top and the base triangles using the formula, Area of the two base triangles = 2 × (1/2 × base of the triangle × height of the triangle) which simplifies to 'base × height' (bh).

The following steps are used to calculate the surface area of a right triangular prism: Observe the following figure which shows a right triangular prism. After expanding this 3-d shape into the 2-d shape we get two right triangles and three rectangles. 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.

#Surface area and volume of triangular prism how to#

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. 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 formula for the surface area of a triangular prism is formed by adding up the area of all the rectangular and triangular faces of a prism. You need just two measurements: the diameter of the base and it's height, but the calculus is more involved than most of the other simple bodies.Formula for Surface Area of Triangular Prism The surface area of a cone is one of the most complicated and it is where the need for a calculator becomes more apparent. The surface area formula for a cone, given its diameter (or radius) and height is π x (diameter / 2) 2 + π x (diameter / 2) x √ ((diameter / 2) 2 + (height 2)), where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is π x radius 2 + π x radius x √ (radius 2 + (height 2)), as seen in the figure below: To find the SA simply multiply 4 times 3.14159 times the radius square.

π is, of course, the well-known mathematical constant, about equal to 3.14159. Visual on the figure below:Ī sphere's surface area can be calculated just by knowing its diameter, or radius (diameter = 2 x radius). The surface area formula for a sphere is 4 x π x (diameter / 2) 2, where (diameter / 2) is the radius of the sphere (d = 2 x r), so another way to write it is 4 x π x radius 2. side 2 is the surface of one of the sides, and since the cube has 6 equal sides, multiplying by 6 gives us the total cube surface area.

This calculation requires only one measurement, due to the symmetricity of the cube. The surface area formula for a cube is 6 x side 2, as seen in the figure below: The result from our surface area calculator will always be a square of the same unit: square feet, square inches, square meters, square cm, square mm. In all surface area calculations, make sure that all lengths are measured in the same unit, e.g. Below are the formulas for calculating surface area of the most common body types. How to calculate the surface area of a body?ĭepending on the type of body, there are different formulas and different required information you need to calculate surface area (a.k.a. How to calculate the surface area of a body?.