How to use this concept
The Volume of a Triangular Prism is calculated by finding the area of the triangular base and then multiplying it by the length of the lateral face.
V=(½) x b x h x l, where b is the base of the triangle, h is the height of the triangle and l is the length of the lateral face. Note: (½) x b x h is the Area of the triangular base.
The Total Surface Area (SA) of the Triangular Prism is calculated by finding the area of the two triangular bases (B) and adding the Lateral Area (LA). The Lateral Area is the sum of the areas of the three rectangles that make up the lateral faces or the perimeter of the triangle multiplied by the length of the lateral face.
SA = 2 x B + LA
B = (½) x b x h = Area of the Triangular Base
LA = P x l = Perimeter x length of lateral surface
Sample Math Problems
Question 1:
Find the volume of a Triangular Prism given the base of the triangle is 5 inches, the height of the triangle is 4 inches and the length of the lateral face is 6 inches.
Answer:
V = (½) x b x h x l = (½) x 5 x 4 x 6 = 60 cubic inches
Question 2:
Provide an image of a triangular prism that has dimensions labeled.
b = 12cm, h = 7cm, l = 4cm
Answer:
V = (½) x b x h x l = (½) x 12 x 7 x 6= 252 cubic cm
Question 3:
Find the surface area of a Triangular Prism given the base has a perimeter of 16 inches and an area of 12 inches squared. The length of the lateral face is 10 inches.
Answer:
B = 12, LA = P x l = 16 x 10 = 160
SA = 2 x B + LA = 2 x 12 + 160 = 184 inches squared
Question 4:
Provide an image of a triangular prism that has dimensions labeled.
Triangle is a right 3, 4, 5 triangle. l = 8
Answer:
B = (½) x b x h = (½) x 3 x 4 = 6
Perimeter of Triangle = 3 + 4 + 5 = 12
LA = P x l = 12 x 8 = 96
SA = 2 x B + LA = 2 x 6 + 96 = 108
