maria is building a carrying case for a musical instrument. The case will have the shape of a triangular prism. She wants to know how much material will be needed to build it. The case will have the dimensions given in the diagram. What is the surface area of the case in square inches?
42
To find the surface area of a triangular prism, we need to find the areas of each of its faces.
The triangular prism consists of two identical triangular bases and three rectangular faces.
First, let's find the area of the triangular bases:
1. The base of the triangle is denoted as B and the height of the triangle is denoted as H. From the diagram, we can see that the base of the triangle is 4 inches and the height is 6 inches.
So, the area of one triangular base is (1/2) * B * H = (1/2) * 4 * 6 = 12 square inches.
Since there are two identical triangular bases, the total area of the bases is 2 * 12 = 24 square inches.
Next, let's find the area of the rectangular faces:
2. The length of each rectangle is the same as the base of the triangle, which is 4 inches.
The width of each rectangle is the same as the height of the triangular base, which is 6 inches.
Therefore, the area of each rectangle is 4 * 6 = 24 square inches.
Since there are three identical rectangular faces, the total area of the rectangular faces is 3 * 24 = 72 square inches.
Finally, let's sum up the areas of the triangular bases and rectangular faces to find the surface area of the triangular prism:
Surface area = Area of bases + Area of faces
= 24 square inches + 72 square inches
= 96 square inches.
Therefore, the surface area of the carrying case for the musical instrument is 96 square inches.