How to solve the total surface area of a rectangular prism with a base of 2.8, a length of 7.1 and a height of 3.2
Total surface area = 2(2.8 x 3.2) + 2(2.8 x 7.1) + 2(3.2 x 7.1)
Total surface area = 22.72 + 39.68 + 22.72
Total surface area = 85.12
To solve for the total surface area of a rectangular prism, you need to find the sum of the areas of all its faces.
1. Start by identifying the faces of the rectangular prism. A rectangular prism has six faces, consisting of a top and bottom face (both having the same area), and four lateral faces (also equal in area).
2. Calculate the area of one of the bases (top or bottom face) by multiplying the base (2.8) with the length (7.1). This gives:
Area of base = base x length = 2.8 x 7.1 = 19.88 square units.
3. Multiply the area of the base by 2 to account for both the top and bottom faces:
Area of both bases = 2 x 19.88 = 39.76 square units.
4. Calculate the area of one of the lateral faces by multiplying the base (2.8) with the height (3.2). This gives:
Area of lateral face = base x height = 2.8 x 3.2 = 8.96 square units.
5. Multiply the area of one lateral face by 4 to account for all four lateral faces:
Area of all lateral faces = 4 x 8.96 = 35.84 square units.
6. Finally, calculate the total surface area by adding the areas of both bases and all lateral faces together:
Total surface area = Area of both bases + Area of all lateral faces
= 39.76 + 35.84
= 75.6 square units.
Therefore, the total surface area of the rectangular prism with a base of 2.8, a length of 7.1, and a height of 3.2 is 75.6 square units.
To find the total surface area of a rectangular prism, you need to add the areas of all six faces. Here are the steps to solve it:
1. Identify the six faces of the rectangular prism. These include the top and bottom faces, which are identical, the front and back faces, and the left and right faces.
2. Calculate the area of the top and bottom faces. The formula for the area of a rectangle is length multiplied by the width. In this case, the length is 7.1 and the width is 2.8. Multiply these two values together to find the area of the top and bottom faces.
Area of top/bottom face = length × width = 7.1 × 2.8
3. Calculate the area of the front and back faces. Similar to step 2, the length is 7.1 and the height is 3.2. Multiply these two values to find the area of the front and back faces.
Area of front/back face = length × height = 7.1 × 3.2
4. Calculate the area of the left and right faces. The width is 2.8 and the height is 3.2. Multiply these two values to find the area of the left and right faces.
Area of left/right face = width × height = 2.8 × 3.2
5. Add up the areas of all six faces to find the total surface area.
Total surface area = 2 × (Area of top/bottom face) + 2 × (Area of front/back face) + 2 × (Area of left/right face)
Plug in the values from the previous steps and calculate the total surface area.