The apothem of a 40-sided regular polygon is 11.7 cm. What is its area if each side measures 1.84 cm?Question 9Select one:a.43.0 cm2b.431 cm2c.17394 cm2d.173.94 cm2
Question
The apothem of a 40-sided regular polygon is 11.7 cm. What is its area if each side measures 1.84 cm?Question 9Select one:a.43.0 cm2b.431 cm2c.17394 cm2d.173.94 cm2
Solution
The area of a regular polygon can be calculated using the formula:
Area = 1/2 * Perimeter * Apothem
Given that the apothem (a) is 11.7 cm, the number of sides (n) is 40, and each side (s) measures 1.84 cm, we can substitute these values into the formula:
Perimeter (P) = n * s = 40 * 1.84 cm = 73.6 cm
Then, substitute P and a into the formula:
Area = 1/2 * P * a = 1/2 * 73.6 cm * 11.7 cm = 430.44 cm^2
So, the closest answer is b. 431 cm^2.
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