Question

The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the sides of a similar quadrilateral whose area is 9 times as great. Put your answer in the same order as the question.

the assignment im working on is area comparsion of polygons

Answer 1

THe ratio of the area of similar figures is always squared. So if the area needs to be 9 times greater, the sides must be 3 times greater (since 3^2 = 9).

So take all four sides and multiply them by 3.

(Volume ratios are cubes in case it comes up later)

Answer 2

3x+4x+5x+6x=9x??????

Answer 3

Imagine you have a square whose sides are all 3. It's area would be 3*3=9.

Now if you had a *simila* square whose sides were twice as big, the sides would now be 6...and the area ofthis new square would be 6*6=36. This area is 4 times the first one...2 squared is 4.

If the similar square had sides that were 4 times as long, the new sides would be 12. THe new area would be 12*12=144 which is 16 times the original.

So anytime you increase the *sides* of a polygon, it's area is increased by the square of that ratio.