The figure below is a net for a rectangular prism. Side a = 70 centimeters, side b = 21 centimeters, and side c = 26 centimeters. What is the surface area of this figure?
First, we need to find the area of each rectangular face. The top and bottom faces each have an area of a * b = 70 * 21 = 1470 square centimeters.
The front and back faces each have an area of a * c = 70 * 26 = 1820 square centimeters.
The left and right faces each have an area of b * c = 21 * 26 = 546 square centimeters.
Now, to find the total surface area, we add up the areas of all six faces:
2 * (a * b) + 2 * (a * c) + 2 * (b * c)
= 2 * 1470 + 2 * 1820 + 2 * 546
= 2940 + 3640 + 1092
= 7672
Therefore, the surface area of the rectangular prism is 7672 square centimeters.
To find the surface area of a rectangular prism, we need to find the areas of each of the six faces and then add them together.
1. Start by calculating the areas of the two bases:
- Base 1: a * b = 70 cm * 21 cm = 1470 cm²
- Base 2: a * b = 70 cm * 21 cm = 1470 cm²
2. Next, calculate the areas of the four lateral faces:
- Face 1: a * c = 70 cm * 26 cm = 1820 cm²
- Face 2: a * c = 70 cm * 26 cm = 1820 cm²
- Face 3: b * c = 21 cm * 26 cm = 546 cm²
- Face 4: b * c = 21 cm * 26 cm = 546 cm²
3. Now, add up all the areas:
- Total Surface Area = 2 * (Base 1 + Base 2) + 2 * (Face 1 + Face 2 + Face 3 + Face 4)
- Total Surface Area = 2 * (1470 cm² + 1470 cm²) + 2 * (1820 cm² + 1820 cm² + 546 cm² + 546 cm²)
- Total Surface Area = 2 * 2940 cm² + 2 * 4732 cm²
- Total Surface Area = 5880 cm² + 9464 cm²
- Total Surface Area = 15344 cm²
Therefore, the surface area of the given rectangular prism is 15344 cm².