Honors Geometry
Chapter 9 Review
Name_______KEY______________
Date_____________Period________
Simplify.
9
1. √32
2. √3
3. 5√50
4√2
√3
25√2
4. √8 + √18 + √32
5.
7
9√2
3
7
6. √52 + 92
√3
√3
√106
Solve for x.
7. 𝑥 2 =
1
9. x 2  6x  4 x
8. x2 – 15 – 2x = 0
9
1
𝑥 = ±3
x = 5, x = -3
x = 0, x = 10

For problems 10-13 use the figure at right.
10. Find the area.
11. Find the circumference.
𝐴𝑟𝑒𝑎 = 𝜋𝑟 2 = 81𝜋
Circumference = 2𝜋𝑟 = 18𝜋
12. Find the length of the arc JK.
13. Find the area of the sector.
18𝜋(30/360) = 1.5𝜋
81π (30/360) =
14. In the given figure, if a = 20
and c = 25, find the value of b.
15. In the given figure, if c = 13 and a = 12,
find the value of b.
25
20
27
4
9
𝜋 = 6.75𝜋
13
12
b = 15
b=5
16. In the given figure, if a=3 and b=4, find the value of c.
32 + 42 = 52, c = 5
c=5
3
4
17. If the length of one leg of a right triangle is 15 and the length of the hypotenuse is 17,
find the length of the other leg. (Hint: Draw a picture!)
82 + 152 = 172, other leg = 8
18. In the given figure, if XY = 10,
find the length of XZ .
10

19. In the given figure, if YZ=10√2, find
the length of XY .

5√2
20
10√2
5√2
20. In the given figure, if AB = 9,
find the length of BC and CA .
9


9
2
21. In the given figure, if BC = 5√3, find
the length of AB and AC .

9
√3
2
5√3
15
22. In the given figure, if AC = 10√3,
find the length of BC and AB .
20
10√3


23. In the given figure, if x = 5, find the
value of w.
10
v = 5√2
w = 2v = 10√2
10√3
24. If the length of a hypotenuse of a right triangle is 5 and the length of a leg is 4, find
the length of the perimeter.
5
4
3
Perimeter = 3 + 4 + 5 = 12
25. Find the value of y.
26. Find the value of x.
27. Solve for z.
z = √10
2
√5
4
x=2
y=4
28. In the figure, what is x?
29. In the figure, solve for y.
y = 4√3
x=6
30. If the length of XY is 4, what is the length of YW?
YW = 2√3√2 = 2√6
4
2√3
2
2√3
31. A Pythagorean rectangle is defined as a rectangle whose length, width, and diagonal
each measure a whole number of units.
a) If AD is 13, what are the dimensions of the rectangle?
5 by 12
b) If AD is 17, what are the dimensions of the rectangle?
8 by 15
32. A square has a diagonal of length 6 2 . What is the perimeter of the square?
perimeter = 24
 square that has a diagonal of length 10?
33. What is the perimeter of the
perimeter = 20√2
34. An altitude of an equilateral triangle is 6 3 units. What is the perimeter of the
equilateral triangle?
perimeter = 36

35. What is the altitude of an equilateral triangle with a perimeter of 30 units?
altitude = 5√3
36. A 30-60-90 right triangle has a long leg of length 7 3 in. What is the area of this
right triangle?
49
Area = 1/2 * base* height = ½ * 7 * 7√3 = 2 √3

37. In the diagram AC is a diameter of the circle and m ACB=45. What is the measure
of arc BC?
arc BC =
90o
38. In the diagram of circle O, m JOL =120 and OL=4 3 in. What is the exact area of
the shaded region?

areaof shaded region = 16𝜋
39. Given circle O with m ROQ =160, find arc PR.

arc PR = 180o – 160o = 20o
40. In the given figure, the slant height is 26 and the altitude of the pyramid is 24. Find
the length of a side of the base of the pyramid.
26
24
10
ID = 2 * 10 = 20