The 2 pentagons above are similar. What is the area of the smaller pentagon?

Solution:

Given 2 similar pentagons

Side of the smaller pentagon is 2.5 in

Side of the bigger pentagon is 7.5 in

Area of the bigger pentagon is 54 sq.in

We know that the principle of similarity states that if two polygons are similar then the ratio of their sides to the area are equal

Side of smaller pentagon/area of the smaller pentagon = side of bigger pentagon/area of the bigger pentagon

Let the area of the smaller pentagon be ‘x’ sq.in

2.5 / x = 7.5 / 54

2.5 /x = 0.138

x = 2.5/0.138

x = 18.11

The area of the smaller pentagon is 18.11 sq.in

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The 2 pentagons above are similar. What is the area of the smaller pentagon?

Summary:

The 2 pentagons above are similar then the area of the smaller pentagon is 18.11 sq.in