What is the lateral area of a right rectangular prism that has rectangular bases measuring 3" by 5" and a height of 6"?
The lateral area of a right rectangular prism can be found by adding up the areas of all the sides except the bases.
The two bases of the prism are rectangles measuring 3" by 5". The area of each base is 3" x 5" = 15 square inches.
The height of the prism is 6", so the lateral sides are two rectangles measuring 6" by 3" and two rectangles measuring 6" by 5".
The area of the two lateral sides measuring 6" by 3" is 6" x 3" = 18 square inches.
The area of the two lateral sides measuring 6" by 5" is 6" x 5" = 30 square inches.
Therefore, the total lateral area of the right rectangular prism is 18 square inches + 30 square inches = <<18+30=48>>48 square inches.
To find the lateral area of a right rectangular prism, we need to calculate the sum of the areas of all the faces, excluding the bases.
In this case, the rectangular prism has a base measuring 3 inches by 5 inches and a height of 6 inches.
Step 1: Calculate the area of one of the bases.
The formula for the area of a rectangle is length times width.
The length is 5 inches and the width is 3 inches.
Area of one base = 5 inches * 3 inches = 15 square inches.
Step 2: Calculate the area of the other base (which has the same dimensions).
Area of the other base = 15 square inches.
Step 3: Calculate the area of the four remaining faces (lateral faces).
Since a rectangular prism has 4 lateral faces, and each face is a rectangle, the area of each face is equal to its height times width.
In this case, the height is 6 inches and the width is 3 inches.
Area of each lateral face = 6 inches * 3 inches = 18 square inches.
Step 4: Calculate the total lateral area by summing the areas of the four lateral faces.
Total lateral area = 4 * 18 square inches = 72 square inches.
Therefore, the lateral area of the right rectangular prism is 72 square inches.