The figure below is a net for a rectangular prism. Side a = 65 centimeters, side b = 24 centimeters, and side c = 18 centimeters. What is the surface area of this figure?
One way to approach this problem is to find the area of each face of the prism and then add them up.
First, let's label the sides of the prism using the net:
- Side 1 has dimensions a x c = 65 x 18
- Side 2 has dimensions b x c = 24 x 18
- Side 3 has dimensions a x b = 65 x 24
To find the surface area, we need to find the area of each face:
- Face 1 and 2 both have areas of a x c = 65 x 18 = 1170
- Face 3 has an area of b x c = 24 x 18 = 432
- The total surface area is the sum of the areas of all faces:
Surface area = 2(1170) + 432 = 2772
Therefore, the surface area of the rectangular prism is 2772 square centimeters.
To find the surface area of the rectangular prism, we need to calculate the area of each face and then add them up.
1. Face 1: This is a rectangle with sides a and b. The area of this face is given by A1 = a * b.
A1 = 65 cm * 24 cm
A1 = 1560 cm^2
2. Face 2: This is another rectangle with sides a and b. The area of this face is also A2 = a * b.
A2 = 65 cm * 24 cm
A2 = 1560 cm^2
3. Face 3: This is a rectangle with sides b and c. The area of this face is given by A3 = b * c.
A3 = 24 cm * 18 cm
A3 = 432 cm^2
4. Face 4: This is another rectangle with sides b and c. The area of this face is also A4 = b * c.
A4 = 24 cm * 18 cm
A4 = 432 cm^2
5. Face 5: This is a rectangle with sides a and c. The area of this face is given by A5 = a * c.
A5 = 65 cm * 18 cm
A5 = 1170 cm^2
6. Face 6: This is another rectangle with sides a and c. The area of this face is also A6 = a * c.
A6 = 65 cm * 18 cm
A6 = 1170 cm^2
To find the total surface area, we add up the areas of all six faces:
Total Surface Area = A1 + A2 + A3 + A4 + A5 + A6
= 1560 cm^2 + 1560 cm^2 + 432 cm^2 + 432 cm^2 + 1170 cm^2 + 1170 cm^2
= 6164 cm^2
Therefore, the surface area of the given rectangular prism is 6164 cm^2.