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A square and a regular pentagon have equal perimeters. If the pentagon has sides of length 12, what is the area of the square?
- a)30
- b)48
- c)60
- d)225
- e)244
Correct answer is option 'D'. Can you explain this answer?
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A square and a regular pentagon have equal perimeters. If the pentagon...
A regular pentagon (5-sided figure) is a pentagon with equal sides and equal angles. If each side of the pentagon has a length of 12, its perimeter is 60. For the square to have a perimeter of 60, each side of the square must have a length of 15. If each side of the square has length of 15, its area is 225.
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A square and a regular pentagon have equal perimeters. If the pentagon...
Perimeter of the pentagon and square
- The perimeter of a regular pentagon with sides of length 12 is 5 * 12 = 60 units.
- Since the square and pentagon have equal perimeters, the square also has a perimeter of 60 units.
Calculating the side length of the square
- For a square, the perimeter is given by 4 * side length.
- Therefore, 4 * side length = 60.
- This gives us the side length of the square as 60 / 4 = 15 units.
Calculating the area of the square
- The area of a square is given by side length squared.
- Therefore, the area of the square = 15 * 15 = 225 square units.
Therefore, the area of the square is 225 square units, which corresponds to option 'D'.
- The perimeter of a regular pentagon with sides of length 12 is 5 * 12 = 60 units.
- Since the square and pentagon have equal perimeters, the square also has a perimeter of 60 units.
Calculating the side length of the square
- For a square, the perimeter is given by 4 * side length.
- Therefore, 4 * side length = 60.
- This gives us the side length of the square as 60 / 4 = 15 units.
Calculating the area of the square
- The area of a square is given by side length squared.
- Therefore, the area of the square = 15 * 15 = 225 square units.
Therefore, the area of the square is 225 square units, which corresponds to option 'D'.
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A square and a regular pentagon have equal perimeters. If the pentagon has sides of length 12, what is the area of the square?a)30b)48c)60d)225e)244Correct answer is option 'D'. Can you explain this answer?
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