Areas of Common Figures

Areas of Common Figures
Project instructions:
This is a first semester exam Geometry ? Formula Sheet
Areas of Common Figures
Rectangle / Square / Parallelogram / Rhombus: A = Triangle: A =
Rhombus: A =
Trapezoid: A = ( )
Regular Polygon: A = Circle: A =
????
Lateral Area
Prism: LA = Cylinder: LA = 2
Pyramid: LA = Cone: LA =
?
Midpoint of a Segment
()
??
Pythagorean Theorem
Surface Area
Prism: SA = Cylinder: SA = 2 + 2
Pyramid: SA =
Cone: SA = Sphere:
?
Volume
()
Prism: V = Cylinder: V =
Pyramid: V = Cone: V = Sphere: V =
???
Geometry Part A First Semester Final Form A Student?s Name:
?Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1.
____ 2.
____ 3.
What is the minimum number of noncollinear points needed to identify exactly one plane? a. one d. four
b. two e.
c. three
None Correct and
?
31? 62?
and
??Point B lies on ? between A and C.
. Find AC.
a. b. c. d.
???????bisects
I H
GLK
. What is the measure of
J
28?
???????????????a. 118? b. 149?
If and ? are vertical angles and
a. 34? b. 17? c. 85? d. 50?
G is between F and H. ? = ? ,
c. d.
???____ 4.
____ 5.
, what is ? ?
?F 4x+14 6x
a. FH = 135
b. FH = 51
c. FH = 22.5
d. FH = 104
G 31 H
= ? ,
and GH = 31. Find FH.
????
?????????????????????????????????????????????????????????????????____ 6.
Find the measure of . Then, classify the angle as acute, right, or obtuse.
??C D
????????????O
B
A
c. m ? ;right
d. m ? ;obtuse
??????a. m ? ;obtuse b. m ? ;acute
____ 7.
____ 8.
For her birthday party, Kelly invited her friends to a nearby roller-skating rink. The area of the rectangular rink is 2,108 ft2, and the length is 68 ft. What is the width of the rink?
a. The width of the rink is 31 ft.
b. The width of the rink is 37 ft.
c. The width of the rink is 34 ft. d. The width of the rink is 40 ft.
Find CD and EF. Then determine if . y
x
?????4
??1
C
?3
?2
D
?E
?????????????????5?4?3?2?1 12345
?5
a. , , b. , ,
c. d.
, , , ,
If an animal is a horse then it has 4 legs. An animal has 4 legs and the animal is a horse.
F
?1
???2
?3
???4
???????????????____ 9.
____ 10.
Write a conditional statement from the statement. A horse has 4 legs.
a. If an animal has 4 legs then it is a horse. c.
b. Every horse has 4 legs. d.
M is the midpoint of ? , A has coordinates (5, 7), and M has coordinates (?1, 2). Find the coordinates of N.
a.
b. (?712,?4)
c. (?7, ?3)
d. (4, 9)
?(2, 412 )
5
?
____ 11.
____ 12.
Write the inverse of the statement, ?If a figure is a square, then it has four sides.?
a. If a figure does not have four sides, then it is not a square.
b. If a figure is not a square, then it does not have four sides.
c. If a figure has four sides, then it is not a square.
d. If a figure has four sides, then it is a square.
Daphne folded a triangular sheet of paper into the shape shown. Find , given , and m .
,
????E
??D
a. = b. = c. = d. = Find .
??C 42o
A61o 22o B
??????????____ 13.
L
(4x + 7)o
(6x – 9)o
118o
???????????____ 14.
KMN
a. = ? b. = ? c. = d. =
For the conditional statement, write the converse and a biconditional statement. If a figure is a right triangle with sides a, b, and c, then ? .
a.
b.
c.
Biconditional: A figure is not a right triangle with sides a, b, and c if and only if
?Converse: If a figure is not a right triangle with sides a, b, and c, then
Biconditional: A figure is a right triangle with sides a, b, and c if and only if Converse: If ? , then the figure is a right triangle with sides a, b, and c. Biconditional: A figure is a right triangle with sides a, b, and c if and only if Converse: If ? , then the figure is not a right triangle with sides a, b, and c.
.
.
.
???d.
Converse: If ? , then the figure is not a right triangle with sides a, b, and c. Biconditional: A figure is a right triangle with sides a, b, and c if and only if
?.
(
____ 15.
____ 16.
____ 17.
Which of the following is a counterexample to the following conjecture? If ? , then ? . a.
b.
c.
d.
Which choice is a counterexample to the conjecture? If x ? 9, then ? .
a. ?7
b. ?12
c. 8
d. 10
e. None correct
Find the area of a trapezoid with parallel sides measuring 5 feet and 10 feet and a height of 3 feet.
?????a. b. c. d.
7.5 150 75 22.5
??????____ 18. In
congruency statement for the triangles.
a. b. c. d.
Find the area of the rhombus.
d1 = (4x + 6) cm
a. b.
What additional information do you need to prove
C BD
A
, ? , ? , and
. In ? , ? , ? , and
. Write the
????____ 19.
???d2 = (8x + 12) cm
c. d.
?????____ 20.
by the SAS Postulate?
??????a. b. c. d.
??
?____ 21.
In
,
.
are medians. Find
.
____ 22.
.
____ 23.
longest.
____ 24.
a.
Find the circumcenter of
c.
= 5.5 d.
?5?4?3?2?1 ?1
B?2 ?3
a.
Write the sides of
1 2 3 4 5x C
(1, 1)
c.
d.
I
58o
62o
K
J
C
XY
O BZA
= 11 b.
= 16.5
with vertices
= 15
A
y
5 4 3 2 1
b. (0, 0)
in order from shortest to
a. b. c. Find the area of the composite figure.
9 ft
12 ft
18 ft
9 ft
d.
a. 216 ft2
b. 297 ft2
c.
378 ft2 d.
540 ft2
????????____ 25.
Find the missing coordinates for the vertex of the rhombus.
____ 28.
Find the measure of each numbered angle.
(0, 0)
(c, 0)
Find CA.
a. b.
CA = 10 CA = 12
c. CA = 14
d. Not enough information. An equiangular
triangle is not necessarily equilateral.
C
2 s ? 10
B
y
(a, d)
(?, ?)
x
??????____ 26.
____ 27.
a. b. c. d.
What is the perimeter of rectangle JKLM with coordinates ? ,
a. 50
b. 15
c. 40
, ? , and ? ?
d. 30
e. None correct
A
?s+2
???31
?
117 2
>
>
???????????????a. m = , m = ? , m =
b. m = ? , m = , m =
c. m = , m = , m = d. m = , m = , m =
????????????____ 29.
Use the diagonals to determine whether a parallelogram with vertices is a rectangle, rhombus, or square. Give all the names that apply.
a. rectangle, rhombus, square
b. rectangle, rhombus
c. rectangle
)
)
)
| |
??????____ 30.
d. square
Find the values of x and y. Express your answers in simplest radical form.
?24 60o
30o
y
x
??a. ,
b., d.,
c. ,
??????31. Jose is walking up a hill toward the top. The distance from the bottom of the hill to the top is 928 feet. How far, in feet, will he have walked when he reaches the midpoint of his walk up the hill?
32. Use inductive reasoning to determine the next term in the series: 8, 12, 11, 15, 14, 18, 17, ____
33. Find the value of x so that . (6x + 5)o
??????????????(5x – 12)o
m
n
???????????34. An isosceles triangle has a perimeter of 50 in. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is the value of x?
35. Amy is painting two murals in her art studio. One is shaped like a trapezoid and the other is shaped like a parallelogram. Use the diagram to find how many square feet Amy will need to paint.
??13 ft 11 ft
22 ft
27 ft 14 ft
????36. The diagram shows the floor of a living room. What area, in square feet, of carpet will be needed to cover the floor?
??????????7 ft
15 ft
15 ft
7 ft
??15 ft
7 ft
7 ft
15 ft
?37. Find the perimeter, in feet, of the composite figure below.
4 ft
3 ft
?????3 ft
3 ft
?4 ft 8 ft
5 ft
38. Find the area of the shaded region in the figure below in square feet. 13 ft
?9 ft
39. Find the perimeter of the triangle. Round your answer to the nearest whole number.
15 45?
40. Find the perimeter of the triangle shown below. Round to the nearest tenth meter.
14 m 45?
41. The area of a rectangular blanket is 33 square feet. The blanket?s length is (3x + 8) feet and the blanket?s width is 3x feet. Find the dimensions of the blanket. Provide a justification for each step.
??42. A banner is shaped like a parallelogram with a diagonal of 3 feet, as shown. Calculate the values of x and y to the nearest hundredth.
x
2x
????????(6y ? 7)? 3 ft
????(4y ? 6)?
43. Find the perimeter of the triangle shown below. Give your answer in simplified radical form.
?30o
y
15 ft 60o
x
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