use the formula to determine the surface area of a right rectangular prism where each edge length measures 12.75 cm.
a. 459 cm^2
b. 5,852.25 cm^2
c. 76.5 cm^2
d. 975.38 cm^2
To calculate the surface area of a right rectangular prism, you need to find the sum of the areas of all the faces.
A right rectangular prism has 6 faces:
- 2 congruent rectangular faces that are parallel to each other and have dimensions (length x width).
- 2 congruent rectangular faces that are parallel to each other and have dimensions (length x height).
- 2 congruent rectangular faces that are parallel to each other and have dimensions (width x height).
In this case, each edge length measures 12.75 cm, so the dimensions are:
Length = 12.75 cm
Width = 12.75 cm
Height = 12.75 cm
The area of each rectangular face can be calculated by multiplying the length and width:
Area of rectangular face 1 = Length x Width = 12.75 cm x 12.75 cm = 162.5625 cm^2
Area of rectangular face 2 = Length x Width = 12.75 cm x 12.75 cm = 162.5625 cm^2
The area of the second set of rectangular faces can be calculated by multiplying the length and height:
Area of rectangular face 3 = Length x Height = 12.75 cm x 12.75 cm = 162.5625 cm^2
Area of rectangular face 4 = Length x Height = 12.75 cm x 12.75 cm = 162.5625 cm^2
The area of the final set of rectangular faces can be calculated by multiplying the width and height:
Area of rectangular face 5 = Width x Height = 12.75 cm x 12.75 cm = 162.5625 cm^2
Area of rectangular face 6 = Width x Height = 12.75 cm x 12.75 cm = 162.5625 cm^2
Now, add up all the areas to find the total surface area:
Total surface area = Area 1 + Area 2 + Area 3 + Area 4 + Area 5 + Area 6
Total surface area = 162.5625 cm^2 + 162.5625 cm^2 + 162.5625 cm^2 + 162.5625 cm^2 + 162.5625 cm^2 + 162.5625 cm^2
Total surface area = 975.375 cm^2
Therefore, the surface area of the right rectangular prism is 975.38 cm^2.
The correct option is d. 975.38 cm^2.