What is the area of a regular pentagon with a side length of 6 units? (2023)

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Question: What is the area of a regular pentagon with a side length of 6 units? (2023)

Options:

Correct Answer: 15√5

Exam Year: 2023

Solution:

The area of a regular pentagon can be calculated using the formula (1/4)√(5(5 + 2√5)) * s². For s = 6, the area is approximately 15√5.

What is the area of a regular pentagon with a side length of 6 units? (2023)

What is the area of a regular pentagon with a side length of 6 units? (2023)

Step 1: Understand that a regular pentagon has 5 equal sides.
Step 2: Identify the side length of the pentagon, which is given as 6 units.
Step 3: Use the formula for the area of a regular pentagon: Area = (1/4)√(5(5 + 2√5)) * s².
Step 4: Substitute the side length (s = 6) into the formula: Area = (1/4)√(5(5 + 2√5)) * 6².
Step 5: Calculate 6², which is 36.
Step 6: Now the formula looks like this: Area = (1/4)√(5(5 + 2√5)) * 36.
Step 7: Calculate the expression inside the square root: 5 + 2√5.
Step 8: Multiply 5 by the result from Step 7.
Step 9: Take the square root of the result from Step 8.
Step 10: Multiply the square root by 36 and then divide by 4 to find the area.
Step 11: The final area is approximately 15√5.

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