Each base of a triangular prism is a right triangle with side lengths 3 inches, 4 inches, and 5 inches. The height of the prism is 7 inches. What is the surface area of the prism?
Answer (3)
Well, each base has 3 4/2=6 square inches. The lateral faces have 3 7, 4 7 and 5 7 as areas, totalling 12*7=84 square inches on the sides. The bases which total 12 sq. in. are added to the sides to get a total surface area of 96 square inches.
The surface area of the triangular prism is: 96 square inches .
To find the surface area of a triangular prism with given dimensions, we start by identifying all the relevant components: the areas of the triangular bases and the areas of the rectangular faces.
1.Calculate the area of one triangular base. Each base is a right triangle with side lengths 3 inches, 4 inches, and 5 inches. The area A of a right triangle is given by:
A = 2 1 × base × height
Here, the base is 3 inches and the height is 4 inches. Thus,
A = 2 1 × 3 × 4 = 6 square inches \[/tex] Since the prism has two identical triangular bases, the total area of the two bases is: \[2 \times 6 = 12 \text{ square inches}\]\\ 2.Calculate the areas of the three rectangular faces. Each rectangular face has one side equal to one of the sides of the triangle and the other side equal to the height of the prism, which is 7 inches. - The first rectangular face has dimensions 3 \times 7\ [tex] Area = 3 × 7 = 21 square inches
The second rectangular face has dimensions 4 \times 7\
Area = 4 × 7 = 28 square inches
The third rectangular face has dimensions 5 × 7 :
Area = 5 × 7 = 35 square inches \[/tex] 3. Sum up the areas of the rectangular faces. [tex] 21 + 28 + 35 = 84 square inches
4.Calculate the total surface area of the prism. Add the total area of the two triangular bases and the total area of the three rectangular faces:
12 + 84 = 96 square inches
Thus, the surface area of the triangular prism is:
96 square inches .
The surface area of the triangular prism is 96 square inches. This is calculated by determining the areas of the triangular bases and the rectangular faces and then summing them up. The triangular bases each have an area of 6 square inches and the three rectangular faces together have an area of 84 square inches.
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