Surface area is the total area of all the surfaces of a 3D object. To find the surface area of the above figure, you would need to calculate the area of each individual face and then add them all together.
Since the figure consists of a rectangular prism and a triangular prism, we need to calculate the surface area for both shapes separately and then add them together.
For the rectangular prism:
- The front and back faces have a length of 4 cm and a height of 7 cm, so the area of each face is 4 cm * 7 cm = 28 cm^2. Since there are two faces, the total area for the front and back faces is 2 * 28 cm^2 = 56 cm^2.
- The top and bottom faces have a width of 3 cm and a height of 7 cm, so the area of each face is 3 cm * 7 cm = 21 cm^2. Since there are two faces, the total area for the top and bottom faces is 2 * 21 cm^2 = 42 cm^2.
- The left and right faces have a length of 4 cm and a width of 3 cm, so the area of each face is 4 cm * 3 cm = 12 cm^2. Since there are two faces, the total area for the left and right faces is 2 * 12 cm^2 = 24 cm^2.
Adding all the areas together, the total surface area for the rectangular prism is 56 cm^2 + 42 cm^2 + 24 cm^2 = 122 cm^2.
For the triangular prism:
- The base of the triangular prism has a width of 3 cm and a height of 7 cm, so the area is 1/2 * 3 cm * 7 cm = 10.5 cm^2.
- There are two triangular faces with the same area, so the total area for the triangular faces is 2 * 10.5 cm^2 = 21 cm^2.
- The two rectangular faces that make up the sides of the prism have a length of 4 cm and a height of 7 cm, so the area of each face is 4 cm * 7 cm = 28 cm^2. Since there are two faces, the total area for the rectangular faces is 2 * 28 cm^2 = 56 cm^2.
Adding all the areas together, the total surface area for the triangular prism is 21 cm^2 + 56 cm^2 = 77 cm^2.
Therefore, the total surface area of the figure is 122 cm^2 (from the rectangular prism) + 77 cm^2 (from the triangular prism) = 199 cm^2.
Find the surface area of the above figure. Remember what surface area is and that will give a clue how to solve the problem
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