A circular field and a square field share equal perimeters. Given the square field's area is 12100 m2, what is the circle's area_________?
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Answer: B. 15400Sq.m
Explanation
The square field area of twelve thousand one hundred square meters means its side length is one hundred ten meters. Multiplying the side length by four gives a square perimeter of four hundred forty meters. Equating this perimeter to the circle gives a circle radius of seventy meters, resulting in an area of fifteen thousand four hundred square meters. Perimeter represents the total outer boundary length for both squares and circles. Circle area is calculated by multiplying pi by the square of its radius. Square area is computed by squaring the length of one of its equal sides.
Land development projects often compare different field shapes sharing identical boundary fencing lengths. Civil engineers analyze geometric properties of plots to optimize space utilization and fencing costs. Geometry applications connect perimeter and area formulas across various two dimensional figures. Option A overestimates the circle area based on an incorrect radius calculation. Option C is incorrect because it does not match the exact calculated area of the circle. Option D underestimates the circular area derived from the four hundred forty meter perimeter.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
- medium
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