Question

The diagram shows corresponding lengths in two similar figures. Find the ratio of the areas of the two figures.

A.7:9
B.14:18
C.163:210
D.49:81

Answer 1

Area of a hexagon = some constant times side^2 = k*a^2, where is the side of the hexagon

Answer 2

Area of big hexagon = k*9^2 = 210 eqn 1
Area of small hexagon = k*7^2 = A (to be determined) eqn 2

Answer 3

Divide eqn 1 by 2:
\[\frac{k \times 9^2}{k\times 7^2} = \frac{210}{A}\]

Answer 4

Solve this for A

Answer 5

I got 3430/27

Answer 6

?

Answer 7

Oh no...We don't need to find the area of the small hexagon explicitly. We want ratio of the two areas..

Answer 8

Would it just be 7:9, or do I have to make a "solve for x" equations with 210^2

Answer 9

That is even simpler.
area of big hexagon / area of small hexagon = k*9^2/k*7^2 = 81/49

Answer 10

Revert it. 49:81

Answer 11

Lol, thanks for all the help! I'm sorry for the misunderstanding.

Answer 12

:)