triangular prism formula for surface area

Then substitute into your formula and solve.Ī P t = ( 6 m × 4 m ) + 3 m ( 5 m + 6 m + 5 m ) A P t = ( 24 m 2 ) + 3 m ( 16 m ) A P t = 24 m 2 + 48 m 2 A P t = 72 m 2 What is the surface area of a rectangular prism?Ī rectangular prism is called a cuboid if it has a rectangular base or a cube if it has a square base with the height of the prism equal to the side of the square base. The total surface area of a triangular prism A Pt isĪnd c is also 5 m (Isosceles triangular base) This would even be more stressful as the number of sides increases.įind the total surface area of the figure below.Ĭalculating the surface area of a triangular prism, Vaia Originals This means we have to calculate the area of each rectangle.

So, the area of the base and top is twice the base area. So, we can say that the total surface area of both the top and base of the prism isĪ B = b a s e a r e a A T = t o p a r e a A T B = A r e a o f b a s e a n d t o p A B = A T A T B = A B + A T A T B = A B + A B A T B = 2 A B The area of the top must surely be the same as the base area which depends on the shape of the base. We have 2 identical sides which take the shape of the prism, and n rectangular sides - where n is the number of sides of the base. Now that we know what the surfaces of a prism comprise, it is easier to calculate the total surface area of a prism. Likewise, a pentagonal base prism will have 5 other sides apart from its identical top and base, and this applies to all prisms.Īn illustration of the rectangular faces of a prism using a triangular prism, Vaia OriginalsĪlways remember that the sides which are different from the top and base are rectangular - this will help you in understanding the approach used in developing the formula. For instance, a triangular base prism will have 3 other sides aside from its identical top and base. It also comprises rectangular surfaces depending on the number of sides the prism base has.

Triangular PrismĪ triangular prism has 5 faces including 2 triangular faces and 3 rectangular ones.Īn image of a triangular prism, Vaia Originals Rectangular PrismĪ rectangular prism has 6 faces, all of which are rectangular.Īn image of a rectangular prism, Vaia Originals Pentagonal PrismĪ pentagonal prism has 7 faces including 2 pentagonal faces and 5 rectangular faces.Īn image of a pentagonal prism, Vaia Originals Trapezoidal PrismĪ trapezoidal prism has 6 faces including 2 trapezoidal faces and 4 rectangular ones.Īn image of a trapezoidal prism, Vaia Originals Hexagonal PrismĪ hexagonal prism has 8 faces including 2 hexagonal faces and 6 rectangular faces.Īn image of a hexagonal prism, Vaia Originals In general, it can be said that all polygons can become prisms in 3D and hence their total surface areas can be calculated.

There are many different types of prisms that obey the rules and formula mentioned above. The total surface area of a prism is the sum of twice its base area and the product of the perimeter of the base and the height of the prism.

Triangular prism formula for surface area