# One side of a polygon measures 10 units. If the measure of the corresponding side of a similar polygon is 6 units, find the ratio of their areas. What is the area of the larger polygon if the area of the smaller polygon is 12 square units?

2
by Cleared

• Brainly User
2016-02-24T15:57:58+08:00
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.)

Solution:
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.

2016-02-27T17:56:51+08:00
One side of a polygon measures 10 units. If the measure of the corresponding side of a similar polygon is 6 units, find the ratio of their areas.
------------
Area is a function of the square of the sides.
Side ratio of 10:6 = 5:3
Area ratio = 25:9

--------------
What is the area of the larger polygon if the area of the smaller polygon is 12 square units?
25:9::Area:12
9*Area = 300
Area = 100/3 sq units