Area

[laney]

Given similar plygons with coresponding sides 6 and 8, what is the area of the smaller if the area of the larger is 64?

The answer is 36 but I can not figure out how they get this. Attempting to study for the General Knowledge Test. Thanks for any help! Please give step by step instructions. Math is not my strongest subject.;-)

 

[Mrspi]

Given similar plygons with coresponding sides 6 and 8, what is the area of the smaller if the area of the larger is 64?

The answer is 36 but I can not figure out how they get this. Attempting to study for the General Knowledge Test. Thanks for any help! Please give step by step instructions. Math is not my strongest subject.;-)

If two figures are similar, then any pair of corresponding sides has the same ratio. In your problem, if ONE pair of corresponding sides has a ratio of 6/8, then any pair of corresponding sides has a ratio of 6/8. And, you can reduce 6/8 to 3/4 if you wish.

If two figures are similar, then the ratio of their areas is the SQUARE of the ratio of any pair of corresponding sides. Since the ratio of any pair of corresponding sides is 6/8 (or 3/4 in reduced form), then the ratio of their areas is (3/4)[sup:3nlcbby4]2[/sup:3nlcbby4] or 9/16.

So, if we let x be the area of the smaller figure, we know that the ratio of the areas is x/64. And that ratio is equal to 9/16.
x/64 = 9/16

Since you may also be asked about volumes of similar solid figures, it might be good to know that the ratio of the volumes of similar figures is the CUBE of the ratio of a pair of corresponding sides.