A right prism has a square base. The perimeter of the base is 24 m. and the height is 10 m. What is the surface area
so the base is 6 m by 6 m.
If we count all 6 surfaces, the
surface area = 2(6x6) + 4(6x10)
= 312 m^2
To find the surface area of a right prism with a square base, we need to calculate the area of each face and then add them together.
Step 1: Calculate the area of the base.
Since the base is a square, we know that all four sides of the square have the same length. The perimeter of the base is given as 24 m, which means each side of the square has a length of 24 m divided by 4, or 6 m.
The formula for the area of a square is side length squared, so the area of the square base is 6 m multiplied by 6 m, which is equal to 36 square m.
Step 2: Calculate the area of the other faces.
A right prism has two identical square faces, one as the base and the other as the top. Therefore, we need to calculate the area of only two of the four rectangular faces.
The formula for the area of a rectangle is length multiplied by width. The length of each rectangle is the same as the perimeter of the base, which is 24 m. The width of each rectangle is the height of the prism, which is 10 m.
So the area of one of the rectangular faces is 24 m multiplied by 10 m, which is equal to 240 square m.
Since there are two identical rectangular faces, the total area of these faces is 2 multiplied by 240 square m, or 480 square m.
Step 3: Calculate the total surface area.
To find the total surface area, we add the area of the base to the area of all four rectangular faces. Since we have the area of the base as 36 square m and the area of the rectangular faces as 480 square m, the total surface area is 36 square m plus 480 square m, which equals 516 square m.
Therefore, the surface area of the right prism is 516 square meters.