Find the latto surface area for the rectangular PENTAGON PRISM represented by the given net. Four feet five feet six feet
To find the lateral surface area of a rectangular pentagonal prism, we need to calculate the area of the five rectangular faces that make up the sides of the prism.
The net provided shows the dimensions of the prism as follows:
- Width of each rectangle: 4 feet
- Height of each rectangle: 5 feet
- Length of the prism: 6 feet
Since there are five rectangles on the lateral surface of the prism, we can calculate the total lateral surface area by adding the areas of each rectangle.
The formula for calculating the area of a rectangle is:
Area = Length x Width
For the rectangular faces of the prism:
- Two rectangles have a length of 6 feet and a width of 4 feet.
- Three rectangles have a length of 6 feet and a width of 5 feet.
First, calculate the area of the two rectangles with dimensions 6 feet by 4 feet:
Area = 6 feet x 4 feet = 24 square feet
Next, calculate the area of the three rectangles with dimensions 6 feet by 5 feet:
Area = 6 feet x 5 feet = 30 square feet
Total lateral surface area = 2(24 square feet) + 3(30 square feet)
Total lateral surface area = 48 square feet + 90 square feet
Total lateral surface area = 138 square feet
Therefore, the lateral surface area of the rectangular pentagonal prism represented by the given net is 138 square feet.