Acertain regular polygon has sides of length 10 cm; its apothem is 12.1 cm. the polygon’s area is 484 cm².
how many sides does the polygon have?
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Given:
Area of polygon = 484 cm²
apothem 12.1 cm
sides of length = 10 cm
no. of sides = x

Area of a regular polygon = 1/2 perimeter * apothem
484 cm² = 1/2 * (10cm * x) * 12.1cm
484 cm² = 6.05cm * 10cm * x
484 cm² = 60.5 cm² * x
484 cm² ÷ 60.5 cm² = x
8 = x

The polygon is an OCTAGON. It has 8 sides.

Perimeter = 10 cm * 8 sides = 80 cm

484cm² = 1/2 * 80cm * 12.1 cm
484cm² = 1/2 * 968 cm²
484 cm² = 484 cm²