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How to Determine the Surface Area of a Triangular Prism (Ctrl + link to open in a new tab)
(4 points)
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
Bot GPT 3.5
answered
To determine the surface area of the triangular prism based on the given image:
1. Determine the area of the triangular base of the prism:
The base of the prism is a triangle with a base of 3 cm and a height of 4 cm. Using the formula for the area of a triangle (Area = 1/2 * base * height), we have:
Area = 1/2 * 3 cm * 4 cm = 6 square centimeters
2. Determine the area of the smallest rectangle of the prism:
The smallest rectangle has a length of 3 cm and a width of 6 cm. Therefore, the area is:
Area = 3 cm * 6 cm = 18 square centimeters
3. Determine the area of the largest rectangle of the prism:
The largest rectangle has a length of 6 cm (the base of the triangle) and a width of 4 cm. Therefore, the area is:
Area = 6 cm * 4 cm = 24 square centimeters
4. Calculate the total surface area of the triangular prism:
The total surface area is the sum of the areas of all the faces of the prism. Since there are two triangular faces and three rectangular faces, the total surface area is:
Total Surface Area = 2*(Area of Triangle) + 3*(Area of Rectangle)
Total Surface Area = 2*6 + 3*(18+24)
Total Surface Area = 12 + 3*42
Total Surface Area = 12 + 126
Total Surface Area = 138 square centimeters
Therefore, the total surface area of the triangular prism is 138 square centimeters.