CK-12 Geometry Concepts

http://www.ck12.org Chapter 10. Perimeter and Area

Answers:

1. First, the ratio of the areas would be

( 3

4

) 2

= 169. Now, we need the area of the larger trapezoid. To find this, we
would multiply the area of the smaller trapezoid by the scale factor. However, we would need to flip the scale factor
over to be^169 because we want the larger area. This means we need to multiply by a scale factor that is larger than
one.A=^169 · 81 = 144 cm^2.

2. The scale factor is

√

25

64

=^58.

3. All you would need to do is multiply the scale factor we found in #2 by 24.

b=

5

8

· 24 = 15 units

Practice

Determine the ratio of the areas, given the ratio of the sides of a polygon.

1.^35
2.^14
3.^72
4. 116

Determine the ratio of the sides of a polygon, given the ratio of the areas.

5. 361


6. 814
   7.^499


7. 14425

This is an equilateral triangle made up of 4 congruent equilateral triangles.

9. What is the ratio of the areas of the large triangle to one of the small triangles?


10. What is the scale factor of large to small triangle?


11. If the area of the large triangle is 20units^2 , what is the area of a small triangle?


12. If the length of the altitude of a small triangle is 2

√

3, find the perimeter of the large triangle.

13. Carol drew two equilateral triangles. Each side of one triangle is 2.5 times as long as a side of the other
    triangle. The perimeter of the smaller triangle is 40 cm. What is the perimeter of the larger triangle?


14. If the area of the smaller triangle is 75cm^2 , what is the area of the larger triangle from #13?


15. Two rectangles are similar with a scale factor of^47. If the area of the larger rectangle is 294in^2 , find the area
    of the smaller rectangle.


16. Two triangles are similar with a scale factor of^13. If the area of the smaller triangle is 22f t^2 , find the area of
    the larger triangle.


17. The ratio of the areas of two similar squares is^1681. If the length of a side of the smaller square is 24 units, find
    the length of a side in the larger square.


18. The ratio of the areas of two right triangles is^23. If the length of the hypotenuse of the larger triangle is 48
    units, find the length of the smaller triangle’s hypotenuse.

Questions 19-22 build off of each other. You may assume the problems are connected.

19. Two similar rhombi have areas of 72units^2 and 162units^2. Find the ratio of the areas.