In two similar polygons, the ratio of their areas is the square of the ratio of their corresponding sides.
Side of the larger polygon: 10 units
Side of the smaller polygon: 6 units
Question A: Find the ratio of the areas.
10:6 is 5:3 in lowest term (Divide each value by its GCF 2.)
Ratio of the area of the similar polygons = (5)² : (3)²
Ratio of the areas = 25 : 9
ANSWER: The ratio of the areas is 25 : 9.
Question B: What is the area of the larger polygon if the smaller polygon's area is 12 sq. units.
Let x be the area of the larger polygon:
25 : 9 = x : 12
(9) (x) = (25) (12)
9x = 300
9x/9 = 300/9
x = 33.33 sq. units
ANSWER: The area of the larger polygon is 33.33 sq. units.