These figures are similar. The perimeter and area of one are given. The perimeter of the
other is also given. Find its area and round
to the nearest tenth.
Perimeter = 20 m
Area = 19.6 m2
Perimeter = 34 m
Area = [? ]m2
Enter

56.644 m^2

Step-by-step explanation:

It's a rule that if the ratio of the sides of 2 similar figures is a:b, the ratio of their areas is a^2:b^2. (I may not be using the standard variables or the exact wording here, but that's the basic idea.)

You can simplify this and understand it with squares. All squares are similar, right? Imagine a 2 in. by 2 in. square and a 4 in. by 4 in. square. The ratio of their sides is 2:4, or 1:2. (The ratio of their perimeters is the same thing. 2*4=8 inches for the smaller square, and 4*4=16 for the bigger square. 8:16=1:2) The ratio of their areas is 4:16, or 1:4. (1/2)^2=1/4

The same thing applies here. The perimeter of the larger figure divided by the perimeter of the smaller one is 34/20=1.7. That means that the area of the larger figure divided by the area of the smaller one is 1.7^2, or 2.89. You can write an equation where x is the area of the larger one:

x/19.6=2.89

x=56.644 m^2

Hope I could help you!

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