Triangular prism
7cm, 7cm, 6cm, 4cm, 12cm
Determine the area of the triangular base of the prism:
square centimeters
Determine the area of the smallest rectangle of the prism.
square centimeters
Determine the area of the largest rectangle of the prism.
square centimeters
What is the total surface area of the triangular prism?
square centimeters?
To determine the area of the triangular base of the prism, we can calculate the area of a triangle with a base of 7 cm and a height of 6 cm.
Area of triangle = (1/2) * base * height
Area = (1/2) * 7 cm * 6 cm
Area = 21 square cm
Next, we determine the areas of the smallest and largest rectangles of the prism.
The smallest rectangle will have dimensions of 4 cm by 7 cm, so the area is:
Area of smallest rectangle = length * width
Area = 4 cm * 7 cm
Area = 28 square cm
The largest rectangle will have dimensions of 7 cm by 12 cm, so the area is:
Area of largest rectangle = length * width
Area = 7 cm * 12 cm
Area = 84 square cm
To find the total surface area of the triangular prism, we need to add the areas of the triangular base, the two rectangles, and the three lateral faces of the prism.
Total surface area = 2*Area of triangle base + Area of smallest rectangle + Area of largest rectangle + 3*(width * height of triangular face)
Total surface area = 2*21 square cm + 28 square cm + 84 square cm + 3*(4 cm * 6 cm)
Total surface area = 42 square cm + 28 square cm + 84 square cm + 72 square cm
Total surface area = 226 square cm
Therefore, the total surface area of the triangular prism is 226 square cm.