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Geometry Mixed Review

Total questions: 50

Worksheet time: 4hrs 10mins

Name
Class
Date
1.

What is the area of the triangle?

a)

17 units2

b)

20 units2

c)

10 units2

d)

16 units2

2.
a)
4 km2
b)
16 km2
c)
64 km2
d)
8 km2
3.

Find the value of h in the parallelogram.

a)

1.6

b)

9.025

c)

10

d)

15.2

4.

Find the value of h in the parallelogram.

a)

7.2

b)

6

c)

5

d)

8.45

5.

Find the value of b if the area of the parallelogram is 12 in2.

a)

2.5

b)

5

c)

2.3

d)

24.96

6.

Which area formula works for this triangle?

a)

1/2(5)(7)cos(49°)

b)

(5)(7)sin(49°)

c)

1/2(5)(7)sin(49°)

d)

all of these

7.

If the sides of a triangle are 12, 5, and 2, what is the area?

a)

12

b)

40.65

c)

19

d)

This triangle does not exist.

8.

Find the area of a trapezoid with bases of 6 feet and 10 feet, and with a height of 6 feet.

a)

60

b)

36

c)

32

d)

48

9.

Megin created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 1.4 m and a height of 2.6 m, how much fertilizer will she need?

a)

3.64 m2

b)

1.82 m2

c)

3.64

d)

1.82

10.

Find the area of the rhombus with diagonals of length 14 and 10

a)

70

b)

35

c)

140

d)

60

11.
The diagonals of a rhombus are
a)
parallel
b)
congruent
c)
perpendicular
d)
equal to the side lengths
12.
A rhombus is a parallelogram with 
a)
four congruent sides
b)
four congruent diagonals
c)
four acute angles
d)
four congruent angles
13.

One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 81 square inches, what are the lengths of the diagonals?

a)

DF = 14 in, EG = 7 in

b)

DF = 18 in, EG = 9 in

c)

DF = 16 in, EG = 8 in

d)

DF = 27 in, EG = 6 in

14.

Find the area of the rhombus.

a)

48 m2

b)

15 m2

c)

24 m2

d)

96 m2

15.
REGULAR in Maths means...
a)
Normal
b)
Two sides have the same length
c)
All sides are equal and all angles are equal
d)
It has right angles
16.

What is the area of a triangle with two sides measuring 5 cm and 8 cm and an included angle of 39°?

a)

15.9 cm²

b)

12.6 cm²

c)

15.3 cm²

d)

16.2 cm²

17.
Which of the following formulas shows the Law of Cosines?
a)
c2 = a2 + b2 - 4ac + cosA
b)
c2 = a2 - b2 - 2abcosC
c)
c2 = a2 + b2 - 2abcosC
d)
(cos A)/a = (cos B)/b
18.

If the sides of a triangle are 8, 8, and 8, what is the area?

a)

8

b)

15.58

c)

27.71

d)

62.91

19.

If the sides of a triangle are 3, 4, and 5, what is the semi-perimeter?

a)

3

b)

6

c)

9

d)

12

20.

Using Heron's Formula, find the area.

a)

35

b)

49

c)

28.9

d)

27.8

21.
What is the correct ratio?
a)
sin 40 = w/28
b)
cos 40 = w/28
c)
tan 40 = w/28
d)
sin 40 = 28/w
22.

Find x, rounded to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

23.

Which law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

24.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express the answer as an exact value.

a)

5π/3

b)

10π/3

c)

10π

d)

40π

25.

What is the area of the shaded region? Leave your answer as an exact value.

a)

25π - 50

b)

25π - 100

c)

5π - 50

d)

5π - 100

26.

What is the area of the green shaded segment?

a)

16π - 64

b)

8π - 32

c)

8π - 64

d)

16π - 32

27.

In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.

a)

5

b)

9

c)

8

d)

6

28.

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the exact area of the rest of Pacman's body?

a)

(464/9)π mm2

b)

(112/9)π mm2

c)

(116/9)π mm2

d)

(28/9)π mm2

29.

Find the length of the bold arc. Leave pi in your answer.

a)

5688π ft

b)

15.8π ft

c)

150.4π ft

d)

54,150 ft

30.

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.

a)

90

b)

60

c)

55

d)

113

31.
The diameter of the face-off circle on an ice-hockey rink is 30 feet. Find its area.
a)
675.6 ft2
b)
29.67 ft2
c)
545.8 ft2
d)
706.5 ft2
32.

Which angles are congruent?

a)

<ACB = <ADB

b)

<ADB = <AEB

c)

<AEB = <ACB

d)

<ACB = <ADB = <AEB

33.

If a quadrilateral is inscribed in a circle, then its ____ angles are _____.

a)

adjacent; complimentary

b)

opposite; complimentary

c)

adjacent; supplementary

d)

opposite; supplementary

34.

A large vintage steam roller that is traveling on a level surface has a wheel with a radius of 3 feet.If the wheel makes a rotation of 110°, about how far will the steam roller travel along the level ground? Round your answer to the nearest tenth of a foot.

35.
A circular swimming pool is 21 feet in diameter.
How many feet around is the pool?
a)
10.5 ft
b)
42 ft
c)
65.94 ft
d)
131.95 ft
36.

Change this log equation into an exponential equation:

34=813^4=81

a)

log⁡34=81\log_34=81

b)

log⁡381=4\log_381=4

c)

log⁡813=4\log_{81}3=4

d)

3 frogs sat on 4 logs and floated away from 81 dogs

37.
Expand
a)
A
b)
B
c)
C
d)
D
38.

Expand

a)

log8x + log8y + log8z

b)

5log8x + 5log8y + 5log8z

c)

log8xy + 5log8z

d)

log8x + log8y + 5log8z

39.

Write as a single logarithm:

log(30) - log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

40.

Rewrite in exponential form:
ln(2) = x

a)

2x = 10

b)

102 = x

c)

ex = 2

d)

e2 = x

41.
All squares are rectangles.
a)
True
b)
False
42.
All rectangles are squares.
a)
True
b)
False
43.

Which quadrilateral(s) have diagonals that bisect opposite angles?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

44.

Which quadrilateral(s) have four right angles?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

45.

Which quadrilateral(s) have perpendicular diagonals?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

46.

Which quadrilateral(s) have diagonals that bisect each other?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

47.

Which quadrilateral(s) have opposite sides that are congruent?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

48.

What are the properties of a rectangle?

a)

Four right angles

b)

Opposite sides are parallel

c)

Opposite sides are congruent

d)

Diagonals bisect each other

e)

Diagonals are congruent

49.

What are the properties of a parallelogram?

a)

Opposite sides are parallel

b)

Diagonals are congruent

c)

Diagonals bisect each other

d)

All sides are congruent

e)

Consecutive angles are supplementary

50.

Which quadrilateral(s) have exactly one pair of parallel sides?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

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