Geo - CH9 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the area of the parallelogram.
____
a. 35 in2
b. 14 in2
2. Find h in the parallelogram.
____
____
c. 21 in2
d. 28 in2
a. 4.8 units
c. 9.6 units
b. 96 units
d. 15 units
3. A store sells circular rugs in three different sizes. The rugs come in diameters of 8 ft, 12 ft, and 16
ft. Find the areas of the three different sizes of rugs. Round to the nearest tenth.
a. 201.1 ft2; 452.4 ft2; 804.2 ft2
c. 50.3 ft2; 113.1 ft2; 201.1 ft2
2
2
2
b. 113.1 ft ; 201.1 ft ; 452.4 ft
d. 50.3 ft2; 201.1 ft2; 452.4 ft2
4. Find the area of a regular hexagon with side length 4 m. Round to the nearest tenth.
____
a. 83.1 m 2
c. 41.6 m 2
b. 24 m2
d. 20.8 m 2
5. Use a composite figure to estimate the area of the irregular shape. The grid has squares with side
lengths of 1 m.
a. 10.5 m2
b. 6.0 m2
____
____
____
c. 17.5 m2
d. 15.0 m2
6. Find the area and perimeter of the polygon with vertices A(−3, 0), B(3, 4), C(5, 1), and D(−1,− 3).
a. area = 26 units2; perimeter = 4 13
c. area = 13 units2; perimeter = 6 13
units
units
2
b. area = 13 units ; perimeter = 4 13
d. area = 26 units2; perimeter = 6 13
units
units
7. A square has a perimeter of 24 cm. If the area of a square is quadrupled and its height remains
constant, what happens to its base length?
a. The base length is multiplied by 4.
c. The base length is increased by 4.
b. The base length is divided by 4.
d. The base length is decreased by 4.
8. A point is chosen randomly on AC. Find the probability that the point is not on AB.
a.
1
4
b. 3
____
c. 6
d.
3
4
9. When a certain SUV travels at 30 mph, it has a stopping distance of 50 feet. If a cardboard box
falls off a truck between 30 to 70 feet in front of this SUV, what is the probability that the SUV
will hit the box?
a. 5
c. 2
7
7
b.
____
1
2
d.
5
4
10. You are designing a target that is a square inside a 48 cm by 72 cm rectangle. What is the length of
a side of the square if the target has a probability of 241 ? What is the length of a side of the square if
the target has a probability of 23 ?
a. 12 cm; 8 cm
b. 12 cm; 48 cm
c. 144 cm; 8 cm
d. 144 cm; 48 cm
Numeric Response
11. A flange is shaped like a square with a circle cut from the center of it. How many square
centimeters is the area of the flange? Round to the nearest hundredth.
12. Suppose the dimensions of a rectangle with a perimeter of 22 inches are tripled. Find the perimeter
of the new rectangle in inches.
Matching
Match each vocabulary term with its definition.
a. apothem
b. center of a circle
c. center of a regular polygon
d. radius
e. circle
f. diameter
g. geometric probability
h. composite figure
i. central angle of a regular polygon
____
____
____
____
13. a method of calculating probability based on a geometric measure such as length or area
14. the point that is equidistant from all vertices of the regular polygon
15. a plane figure made up of triangles, rectangles, trapezoids, circles, and other simple shapes, or a
three-dimensional figure made up of prisms, cones, pyramids, cylinders, and other simple threedimensional figures
16. an angle whose vertex is the center of the regular polygon and whose sides pass through
consecutive vertices
____
____
____
17. the point inside a circle that is the same distance from every point on the circle
18. the perpendicular distance from the center of a regular polygon to a side of the polygon
19. the set of points in a plane that are a fixed distance from a given point
Geo - CH9 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: D
Step 1 Use the Pythagorean Theorem to find the height h.
32 + h2 = 52
h = 4 in2
Step 2 Use h to find the area of the parallelogram.
Area of a parallelogram
A = bh
A = (7)(4)
Substitute 7 for b and 4 for h.
2
Simplify.
A = 28 in
Feedback
A
B
C
D
Use the Pythagorean Theorem to find the height. Multiply this by the base.
Use the Pythagorean Theorem to find the height. Multiply this by the base.
Use the Pythagorean Theorem to find the height. Multiply this by the base.
Correct!
PTS: 1
DIF: Basic
REF: Page 589
OBJ: 9-1.1 Finding Measurements of Parallelograms
NAT: 12.2.1.h
TOP: 9-1 Developing Formulas for Triangles and Quadrilaterals
2. ANS: C
Step1 Find the area of the parallelogram.
The area of the parallelogram is twice the area of a right
A = 16(12) = 192
triangle with base 12 and height 16.
Step2 Use the result to find h.
The area of the parallelogram is equal to the area of a
20h = 192
rectangle with height h and width 20.
Solve.
h = 9.6
Feedback
A
B
C
D
Find the area of a right triangle with base 12 and height 16. Compare that to the
area of a rectangle with height h and width 20.
Find the area of a right triangle with base 12 and height 16. Compare that to the
area of a rectangle with height h and width 20.
Correct!
Find the area of a right triangle with base 12 and height 16. Compare that to the
area of a rectangle with height h and width 20.
PTS: 1
DIF: Advanced
NAT: 12.3.3.f
TOP: 9-1 Developing Formulas for Triangles and Quadrilaterals KEY: multi-step
3. ANS: C
2
The area of a circle is πr , and the radius is half of the diameter.
2
2
The area of the 8-ft rug: A = π(4) ≈ 50.3 ft
2
2
The area of the 12-ft rug: A = π(6) ≈ 113.1 ft
2
2
The area of the 16-ft rug: A = π(8) ≈ 201.1 ft
Feedback
A
B
C
D
Use the radius to find the area.
Use the radius to find the area.
Correct!
Use the same method you used to find the area of the smallest rug to find the
areas of the other rugs.
PTS: 1
DIF: Average
REF: Page 601
OBJ: 9-2.2 Application
NAT: 12.2.1.h
TOP: 9-2 Developing Formulas for Circles and Regular Polygons
KEY: area | circle
4. ANS: C
The perimeter is 6(4) = 24 m. The hexagon can be divided into 6 equilateral triangles with side
length 4 m. By the 30º-60º-90º Triangle Theorem, the apothem is 2 3 m.
A = 12 aP
Area of a regular polygon
A = 12 (2 3)( 24 )
Substitute 2 3 for a and 24 for P.
Simplify.
A = 24 3 ≈ 41.6 m2
Feedback
A
B
C
D
Divide your answer by 2.
Divide the perimeter by the apothem. To find the apothem, multiply half of one
side by the square root of 3.
Correct!
Multiply your answer by 2.
PTS: 1
DIF: Average
REF: Page 602
OBJ: 9-2.3 Finding the area of a Regular Polygon
NAT: 12.2.1.h
TOP: 9-2 Developing Formulas for Circles and Regular Polygons
5. ANS: A
Draw a composite figure that approximates the irregular shape. Find the area of each part of the
composite figure.
Area of triangle I:
A = 12 bh = 12 (4)(1) = 2 m2
Area of triangle II:
A = 12 bh = 12 (1)(4) = 2 m2
Area of triangle III:
A = 12 bh = 12 (2)(3) = 3 m2
Area of triangle IV:
A = 12 bh = 12 (1)(1) = 0.5 m2
Area of rectangle V:
A = bh = (3)(1) = 3 m2
Area of composite figure:
2 + 2 + 3 + 0.5 + 3 = 10.5 m2
2
The area of the irregular shape is about 10.5 m .
Feedback
A
B
C
D
Correct!
Draw a composite figure that approximates the irregular shape. Find the area of
each part of the composite figure.
Draw a composite figure that approximates the irregular shape. Find the area of
each part of the composite figure.
Draw a composite figure that approximates the irregular shape. Find the area of
each part of the composite figure.
PTS: 1
DIF: Average
REF: Page 608
OBJ: 9-3.4 Estimating Areas of Irregular Shapes
TOP: 9-3 Composite Figures
6. ANS: D
Step 1 ABCD appears to be a rectangle.
To verify this, show that the sides are
perpendicular.
0
slope of AB = 3 4−−(−3)
= 46 = 23
slope of BC= 15 −− 43 = − 32
−1
−4
2
slope of CD = −3
−1 − 5 = −6 = 3
0
slope of DA= −1−3−−(−3)
= − 32
The consecutive sides are perpendicular,
so ABCD is a rectangle.
NAT: 12.2.1.h
Step 2 Let CD be the base and AD be the height of the rectangle. Use the Distance Formula to find
each side length.
CD =
(5 − (−1))2 + (1 − (−3))2 =
AD =
(−3 − (−1))2 + (0 − (−3))2 =
52 = 2 13 units
13 units
The area of ABCD is A = bh = ( 13 )(2 13 ) = 26 units2.
The perimeter of ABCD is P = AB + BC + CD + AD = 6 13 units.
Feedback
A
B
C
D
Check for algebra mistakes.
To find the length of a segment, use the Distance Formula.
To find the length of a segment, use the Distance Formula.
Correct!
PTS: 1
DIF: Average
REF: Page 617
OBJ: 9-4.2 Finding Perimeter and Area in the Coordinate Plane NAT: 12.2.1.h
TOP: 9-4 Perimeter and Area in the Coordinate Plane
7. ANS: A
Since the square has a perimeter of 24 cm, each side length is 6 cm.
The area of a square is its base multiplied by its height. Since the height remains constant, if its
area is quadrupled, the original base length is multiplied by 4.
Feedback
A
B
C
D
Correct!
If the area changes and the height remains constant, the base must change in the
same manner.
The new area is a multiple of the original area.
The new area is a multiple of the original area.
PTS:
OBJ:
TOP:
8. ANS:
1
DIF: Average
REF: Page 623
9-5.3 Effects of Changing Area
NAT: 12.2.1.h
9-5 Effects of Changing Dimensions Proportionally
A
PÊÁ not on AB ˆ˜ = 1 −
Ë
¯
AB
AC
= 1 − 68 =
2
8
=
1
4
Feedback
A
B
C
Correct!
Find the probability of the point being on AB, namely (AB)/(AC). Subtract this
from 1.
Find the probability of the point being on AB, namely (AB)/(AC). Subtract this
from 1.
D
Subtract this answer from 1.
PTS: 1
DIF: Basic
REF: Page 630
OBJ: 9-6.1 Using Length to Find Geometric Probability
NAT: 12.4.4.b
TOP: 9-6 Geometric Probability
9. ANS: B
The probability of an event occurring is the interval of the required outcome divided by the total
interval.
Create a number line that depicts the possible distance from the box to the SUV and the stopping
distance of the SUV.
From the number line, it appears that, of a total of 40 feet over which the box may fall, the first 20
feet will force the SUV to hit the box. Thus the probability that the SUV will hit the box is
P(SUV hits box)= Interval for collision to occur = 20 = 1 .
Total interval where box may fall 40 2
Feedback
A
B
C
D
The probability is the interval of the required outcome divided by the total
interval.
Correct!
The probability is the interval of the required outcome divided by the total
interval.
The probability is the interval of the required outcome divided by the total
interval.
PTS: 1
DIF: Average
REF: Page 631
OBJ: 9-6.2 Application
NAT: 12.4.4.j
TOP: 9-6 Geometric Probability
10. ANS: B
The area of the 48 cm by 72 cm rectangle is 48(72) = 3, 456 cm2.
The area of the first square is 241 (3456) = 144 cm2. A side of the square is 12 cm.
The area of the second square is
2
3
(3456) = 2304 cm2. A side of the square is 48 cm.
Feedback
A
B
C
A square with sides measuring 8 cm is smaller than a square with sides
measuring 12 cm.
Correct!
A square with sides measuring 144 cm is larger than the rectangle.
D
A square with sides measuring 144 cm is larger than the rectangle.
PTS: 1
DIF: Advanced
TOP: 9-6 Geometric Probability
NAT: 12.4.4.b
NUMERIC RESPONSE
11. ANS: 525.76
PTS: 1
12. ANS: 66
DIF:
Advanced
NAT: 12.2.1.c
TOP: 9-3 Composite Figures
PTS: 1
DIF: Average
NAT: 12.2.1.c
TOP: 9-5 Effects of Changing Dimensions Proportionally
MATCHING
13. ANS:
TOP:
14. ANS:
TOP:
15. ANS:
TOP:
16. ANS:
TOP:
17. ANS:
TOP:
18. ANS:
TOP:
19. ANS:
TOP:
G
PTS: 1
DIF: Basic
REF:
9-6 Geometric Probability
C
PTS: 1
DIF: Basic
REF:
9-2 Developing Formulas for Circles and Regular Polygons
H
PTS: 1
DIF: Basic
REF:
9-3 Composite Figures
I
PTS: 1
DIF: Basic
REF:
9-2 Developing Formulas for Circles and Regular Polygons
B
PTS: 1
DIF: Basic
REF:
9-2 Developing Formulas for Circles and Regular Polygons
A
PTS: 1
DIF: Basic
REF:
9-2 Developing Formulas for Circles and Regular Polygons
E
PTS: 1
DIF: Basic
REF:
9-2 Developing Formulas for Circles and Regular Polygons
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