1. Find the surface area of a triangular prism with the following dimensions: base length = 4 cm, base height = 6 cm, prism height = 8 cm.
First, we need to find the area of the triangular base:
Area = 1/2 x base length x base height
Area = 1/2 x 4 cm x 6 cm
Area = 12 cm^2
Next, we need to find the lateral area of the prism:
Lateral area = perimeter of base x prism height
Perimeter of base = sum of all 3 sides of the triangle
Perimeter = 4 cm + 4 cm + 6 cm
Perimeter = 14 cm
Lateral area = 14 cm x 8 cm
Lateral area = 112 cm^2
Finally, we can find the total surface area by adding the area of the base and the lateral area:
Surface area = area of base + lateral area
Surface area = 12 cm^2 + 112 cm^2
Surface area = 124 cm^2
Therefore, the surface area of the triangular prism is 124 cm^2.
2. Find the volume of a triangular pyramid with the following dimensions: base length = 5 cm, base height = 8 cm, pyramid height = 10 cm.
First, we need to find the area of the triangular base:
Area = 1/2 x base length x base height
Area = 1/2 x 5 cm x 8 cm
Area = 20 cm^2
Next, we need to find the volume of the pyramid:
Volume = 1/3 x base area x height
Volume = 1/3 x 20 cm^2 x 10 cm
Volume = 66.67 cm^3
Therefore, the volume of the triangular pyramid is 66.67 cm^3.
Use nets to solve triangular problems practice math 6B
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