Question

The sides of two similar trapezoids are in a ratio of 1:3. The area of the smaller trapezoid is 12 squared inches. Find the area of the larger trapezoid

Answer 1

The area of the larger square is 4 times larger than the area of the smaller square.

Step-by-step explanation:

First, find the dimensions of the larger square. The problem states that the dimensions are twice the first square. You can use this information to figure out the scale factor, and this means they are scaled up by a factor of 2. The side length of the larger square is: 4 inches x 2 = 8 inches.

Then, compare the two areas. You want to know how the area of the larger square compares to the area of the smaller square. Write a ratio comparing the two areas. The answer is 4. The area of the larger square is 4 times larger than the area of the smaller square. This leads to a rule when comparing areas of similar figures. The ratio of areas of similar figures is the square of the scale factor.

Answer 2

108 sq in.

Step-by-step explanation:

The ratio of the areas is the square of the ratio of the sides.

Side ratio 1:3

Area ratio 1:9

The side of the larger trapezoid is 3 times the side of the smaller trapezoid.

The area of the larger trapezoid is 9 times the area of the smaller trapezoid.

9 * 12 sq in. = 108 sq in.