The lateral area of a prism is the surface area of all sides, or faces, that are not the base. [3] X Research source
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: 6+5+4=15{\displaystyle 6+5+4=15}. So, the perimeter of one base is 15 cm.
For example, L=15h{\displaystyle L=15h}.
For example, if the height of the prism is 9 cm, your formula will look like this: L=15(9){\displaystyle L=15(9)}.
For example, 15(9)=135{\displaystyle 15(9)=135}, So, the lateral surface area of the prism is 135 square centimeters.
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 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.
For example, if the base of the triangle is 6 cm, your formula will look like this: A=126h{\displaystyle A={\frac {1}{2}}6h}.
For example, if the height is 3. 3 cm, then your calculations will look like this: A=126(3. 3){\displaystyle A={\frac {1}{2}}6(3. 3)}A=3(3. 3){\displaystyle A=3(3. 3)}A=9. 9{\displaystyle A=9. 9}So, the area of the base is 9. 9 square centimeters.
For example, if the lateral area of your triangular prism is 135 square centimeters, your formula will look like this: SA=135+2B{\displaystyle SA=135+2B}.
For example, if the area of one base of your prism is 9. 9 square centimeters, your formula will look like this: SA=135+2(9. 9){\displaystyle SA=135+2(9. 9)}.
For example:SA=135+2(9. 9){\displaystyle SA=135+2(9. 9)}SA=135+19. 8{\displaystyle SA=135+19. 8}SA=154. 8{\displaystyle SA=154. 8}So, the surface area of a triangular prism with a base having sides measuring 6, 5, and 4 centimeters in length, and a height measuring 9 centimeters in length, has a surface area of 154. 8 square centimeters.
