The figure below is a net for a rectangular prism. Side a = 18 centimeters, side b = 10 centimeters, and side c = 6 centimeters. What is the surface area of this figure?
To find the surface area of the rectangular prism, we need to calculate the areas of all six faces and sum them up.
The rectangular prism has three pairs of congruent faces.
The area of the first pair is a * b = 18 * 10 = 180 square centimeters.
The area of the second pair is a * c = 18 * 6 = 108 square centimeters.
The area of the third pair is b * c = 10 * 6 = 60 square centimeters.
To find the total surface area, we sum the areas of all six faces:
Total surface area = 2 * (a * b + a * c + b * c)
Total surface area = 2 * (180 + 108 + 60)
Total surface area = 2 * 348
Total surface area = 696 square centimeters.
Therefore, the surface area of the rectangular prism is 696 square centimeters.
To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then sum them up.
Given the dimensions a = 18 cm, b = 10 cm, and c = 6 cm, let's label the faces accordingly:
- Face 1: Upper face with dimensions a x b
- Face 2: Lower face with dimensions a x b
- Face 3: Front face with dimensions a x c
- Face 4: Back face with dimensions a x c
- Face 5: Left side face with dimensions b x c
- Face 6: Right side face with dimensions b x c
To calculate the area of each face, we multiply the length and width of that face:
- Face 1: Area = a x b = 18 cm x 10 cm = 180 cm²
- Face 2: Area = a x b = 18 cm x 10 cm = 180 cm²
- Face 3: Area = a x c = 18 cm x 6 cm = 108 cm²
- Face 4: Area = a x c = 18 cm x 6 cm = 108 cm²
- Face 5: Area = b x c = 10 cm x 6 cm = 60 cm²
- Face 6: Area = b x c = 10 cm x 6 cm = 60 cm²
Now, we sum up the areas of all the faces to find the total surface area:
Surface Area = Face 1 + Face 2 + Face 3 + Face 4 + Face 5 + Face 6
Surface Area = 180 cm² + 180 cm² + 108 cm² + 108 cm² + 60 cm² + 60 cm²
Surface Area = 696 cm²
Therefore, the surface area of the given rectangular prism is 696 square centimeters.