Calculate the total surface area of a pentagonal prism with a length of 20 cm and a width of 20 cm. The cross - section of a regular pentagon of area 688.2 cm².
To calculate the total surface area of a pentagonal prism, we need to find the surface area of the two pentagonal bases and the five rectangular faces.
The area of the pentagon is given as 688.2 cm², which is the area of one base. Since the prism has two bases, the total area of the two pentagonal bases is 2 * 688.2 = 1376.4 cm².
The length of the prism is given as 20 cm, and the width is also 20 cm. Therefore, the height of each rectangular face is also 20 cm.
The total surface area of a rectangular face can be calculated using the formula: A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
For the pentagonal prism, the rectangular faces have dimensions 20 cm (length), 20 cm (width), and 20 cm (height).
Therefore, the total surface area of the five rectangular faces is: 5 * (2(20)(20) + 2(20)(20) + 2(20)(20)) = 5 * (400 + 400 + 400) = 5 * 1200 = 6000 cm².
Finally, to find the total surface area of the pentagonal prism, add the surface area of the two bases to the surface area of the five rectangular faces: 1376.4 + 6000 = 7376.4 cm².
So, the total surface area of the pentagonal prism is 7376.4 cm².
The answer is 3376 cm²
I apologize for the mistake in the previous response. Let's recalculate the total surface area of the pentagonal prism.
The area of the pentagon is given as 688.2 cm², which is the area of one base. Since the prism has two bases, the total area of the two pentagonal bases is 2 * 688.2 = 1376.4 cm².
The length of the prism is given as 20 cm, and the width is also 20 cm. Therefore, the height of each rectangular face is also 20 cm.
The total surface area of a rectangular face can be calculated using the formula: A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
For the pentagonal prism, the rectangular faces have dimensions 20 cm (length), 20 cm (width), and 20 cm (height).
Therefore, the total surface area of the five rectangular faces is: 5 * (2(20)(20) + 2(20)(20) + 2(20)(20)) = 5 * (400 + 400 + 400) = 5 * 1200 = 6000 cm².
Finally, to find the total surface area of the pentagonal prism, add the surface area of the two bases to the surface area of the five rectangular faces: 1376.4 + 6000 = 7376.4 cm².
So, the correct total surface area of the pentagonal prism is 7376.4 cm², not 3376 cm² as previously stated.