formula for surface area of triangular prisms

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, StudySmarter 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, StudySmarter Originals Rectangular PrismĪ rectangular prism has 6 faces, all of which are rectangular.Īn image of a rectangular prism, StudySmarter Originals Pentagonal PrismĪ pentagonal prism has 7 faces including 2 pentagonal faces and 5 rectangular faces.Īn image of a pentagonal prism, StudySmarter Originals Trapezoidal PrismĪ trapezoidal prism has 6 faces including 2 trapezoidal faces and 4 rectangular ones.Īn image of a trapezoidal prism, StudySmarter Originals Hexagonal PrismĪ hexagonal prism has 8 faces including 2 hexagonal faces and 6 rectangular faces.Īn image of a hexagonal prism, StudySmarter 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. All the other cases can be calculated with our triangular prism calculator.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. 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) 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).

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.

Formula for surface area of triangular prisms