The figure below is a net for a rectangular prism. Side a = 69 centimeters, side b = 24 centimeters, and side c = 18 centimeters. What is the surface area of this figure?
We can find the surface area of the rectangular prism by summing the areas of all six faces. Looking at the net, we can see that there are two rectangles with dimensions a by b, two rectangles with dimensions b by c, and two rectangles with dimensions a by c.
The area of a rectangle is given by its length multiplied by its width, so the area of each rectangle is:
- a*b = 69cm * 24cm = 1656 cm²
- b*c = 24cm * 18cm = 432 cm²
- a*c = 69cm * 18cm = 1242 cm²
To find the total surface area, we add up all six areas:
1656 cm² + 1656 cm² + 432 cm² + 432 cm² + 1242 cm² + 1242 cm² = 7060 cm²
Therefore, the surface area of the rectangular prism is 7060 square centimeters.