How Do You Find the Lateral and Surface Areas of a Triangular Prism?

h₁ is the height of the triangular base, h₂ is the height of the prism
L₁ and L₂ are the lengths of the legs of the triangular base
'b' is the length of the base of the triangular base
The lateral area, 'L', is the perimeter of the base, 'P', times the height of the prism
'B' stands for the area of the triangular base
The surface area, 'S', is the lateral area plus the area of the bases

1. The lateral area is the sum of all the faces that are not bases
1. We can find 'P', the perimeter of the base, by adding together the three sides of the triangle
2. So we add 12.2+4.7+7.9 to get P=24.8
3. Then we multiply by the height of the prism, 20 cm, to find 'L', the lateral area
4. Multiplying 24.8 by 20 gives us the lateral area: L=496 cm²
1. Both bases are triangles
1. Both bases are triangles
2. Congruent triangles have the same area
3. Remember, the formula for the area of a triangle is (1/2)bh, where 'b' is the base and 'h' is the height
4. In our diagram, the base of the triangular base is represented by 'h₁
1. Surface area is equal to the lateral area plus the area of the bases
1. L, the lateral area, we found to be 496
2. We also found that B, the area of one of the bases, is 7.9
3. Since the bases are congruent, we can just multiply 7.9 by 2 and then add 496, the lateral area
4. This will give us the surface area of the prism

Find the lateral and surface areas of the triangular prism