What is the total surface area of the triangular prism? square centimeters 6cm 7cm 7cm 4cm 12cm
To find the total surface area of a triangular prism, we need to calculate the areas of the two triangular bases and the three rectangular sides.
1. Calculate the area of the two triangular bases:
Area of a triangle = 1/2 * base * height
Base = 7cm
Height = 4cm
Area of one triangle = 1/2 * 7cm * 4cm = 14 square centimeters
Total area of two triangles = 2 * 14 square centimeters = 28 square centimeters
2. Calculate the areas of the three rectangular sides:
Side 1:
Length = 7cm
Height = 6cm
Area of side 1 = length * height = 7cm * 6cm = 42 square centimeters
Side 2:
Length = 7cm
Height = 6cm
Area of side 2 = length * height = 7cm * 6cm = 42 square centimeters
Side 3:
Length = 12cm
Height = 4cm
Area of side 3 = length * height = 12cm * 4cm = 48 square centimeters
Total area of three sides = 42 square centimeters + 42 square centimeters + 48 square centimeters = 132 square centimeters
3. Add the areas of the two triangular bases and the three rectangular sides to find the total surface area:
Total surface area = 28 square centimeters + 132 square centimeters = 160 square centimeters
Therefore, the total surface area of the triangular prism is 160 square centimeters.