Shape and Space · Math-Aids.Com. Name: Date: 5. 1 The Area of a Parallelogram Develop and apply...
Transcript of Shape and Space · Math-Aids.Com. Name: Date: 5. 1 The Area of a Parallelogram Develop and apply...
I
Shape and Spacebevelop and apply a formula for determining the area of:
• Triangles• Parallelograms• Circles
bemonstrate an understanding of circles by:
• bescribing the relationships among radius, diameter and circumference• Relating circumference to pi• betermining the sum of central angles• Constructing circles with a given radius or diameter• Solving problems involving radii, diameters and circumferences of circles.
u Perform geometric constructions, including:
• Perpendicular line segments• Parallel line segments• Perpendicular bisectors• Angle bisectors.
E Identify and plot points in the four quadrants of the Cartesian plane, using
integral, ordered pairs.
Perform and describe transformations (translations, rotations and
reflections) of a 2b shape in all four quadrants of a Cartesian plane.
Some Terms You Should Know
parallel: lines that travel in the same direction and never intersect
perpendicular: meeting at a 900 angle
1
parallelogram: a four sided polygon with opposite sides parallel aridequal in length.
base: the bottom edge of a polygon
height: the length of the line perpendicular to the base that meetsthe opposite line of the polygon
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PARTS OF A CIRCLE:
Diameter:
Radius:
Pi (ir)
Shape Formula Examples
Name: Score:
Teacher--_
Date:
Identify and Calculate the Area and Perimeter for each Quadrilateral.
a = 64.42 cm
c=95cm h=59cma = 54.43 cmc=87cm h=52cm
a = 51.62cm
c=8lcm h=47cm
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
4)
a = 45.56 cm
c=88cm h4lcma = 61 cmc=9lcm h=58cm
6)
a = 49.66 cmc=99cm h=46cm
Area:
Perimeter:
Type:
7)
a 60.55 cm
c89cm h57cm
Area:
_____________
Perimeter:
_____________
Type:
_____________
8)7
a =49.71cm
c80cm h=45cm
Area:
Perimeter:
Type:
9)
a = 52.33 cm
c=82cm h=49cm
Area:
_______________
Pen meter:
_______________
Type:
_____________
U Math-Aids.Com
1)
C
2) /1/h / a/7
C C
>45)
/C C
C
Area:
jerimeter:
Type:
C
Area:
Perimeter:
Type:
Name:
Teacher
Score:
Date:
Identify and Calculate the Area and Perimeter for each Quadrilateral.
1)
a = 5.18cm
c=8cm h4.8cma = 5.23 cmc=9.9cm h=4.9cm
a = 5.9 cm
c = 8.7 cm
Area:
Perimeter:
Type:
4)
a = 5.63 cm
c=8.5cm h=5.3cm
Area:
Perimeter:
Type:
6),/
a 6.41 cm
c8.9cm h=5.9cm
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
a = 5.36 cmc=9.lcm h5.lcm
a=5.58cm
c=8.2cm h=5.2cma = 4.94 cm
c=8.6cm h=4.5cm
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
2)
C
3)
C C
h = 5.4 cm
Area:
Perimeter:
_______________
Type:
5)
a=5.52cmc=9.7cm h=5cm
7) 8) 9)
Area:
______________
Perimeter:
_______________
Type:
____________
Math-Aids.Com
Name: Date:
5. 1 The Area of a Parallelogram
Develop and apply the formula for the area of aparallelogram.
j\t-Home HelpThe height is a line segmentdrawn to form a right angle withone side of a shape.
The base is the side of a shapethat is measured to calculate thearea or perimeter of the shape;any side of a shape can be thebase of the shape.
For example,
/eiht
/base
The formula for the area of aparallelogram with base b andheight Ii is A = b x h.
3. a) Estimate the area of each parallelogram, in square units,by counting the squares.
/A./
/::B;:
b) Calculate the area of each parallelogram, in square units,using a formula.
j1. Fill in the blanks for the parallelogram below.
A / height
_______________
/ — 4 units // / base
_______
6 unitsarea
___________________
2. Complete the table.
Area ofBase Height Parallelograma) 3cm 5cm
b) 2m 16m2
C) 6cm 30cm2
d) 5.3m 3.2m
e) 2.4 mm 3.6 mm2
f) 1.2 dm 0.6 dm2
Copyright © 2008 by Nelson Education Ltd. Chapter 5: Measurement 45
Name: Score:Teacher Date:
Identify and Calculate the Area and Perimeter for each Triangle.
2)
a=79cm b5lcm
c = 94.03 cm
a=88cm b=43cm
c = 97.94 cm
a=82cm b=59cm
c = 101.02cm
bL
Area:
Perimeter:
Type:
b
Area:
Perimeter:
Type:
6)
a76cm b45cm
c = 88.32 cm
a=73cm b=58cm
c = 93.24 cm
a=84cm b=47cm
c = 96.25 cmArea:
Perimeter:
Type:
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
b8)
bE<
9)
aa=9Ocm b6Ocm
c 108.17cma=8lcm b=4lcm
c = 90.79 cm
Area:
_________
Perimeter:
__________
Type:
__________
a77cm b=5Ocm
c=91.81 cm
Area:
__________
Perimeter:
__________
Type:
_________
1)
b%<
a a
b
Area:
Perimeter:
Type:
4) 5)
C
Area:
Perimeter:
jpe:
DI-Dj Math-Aids.Com
Name Score:Teacher Date:
Identify and Calculate the Area and Perimeter for each Triangle.
b
2) 3)
a
a=9cm b4.9cm
C = 10.25cm
a=7.lcm b=4.lcm
c = 8.2 cm
a=7.5cm b=4.6cm
c = 8.8 cm
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
4)
bEN
5) 6)
a7.3cm b=5.7cm
c = 9.26 cm
a=5.92cm b=8.42cm
c8.2cm h=5.6cm
a=4.83cm b=8.44cm
c9.2cm h=4.4cm
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
Area:
Perimeter:
Type:
8) 9)
a = 5.97 cm b = 8.27 cm
c8.5cm h5.5cm
Area:
____________
Perimeter:
_____________
Type:
____________
a=8.6cm b=4cm
c = 9.48 cm
Area:
_________
Perimeter:
_________
Type:
_________
a=6.33cm b=8.45cm
c9cm h=5.7cm
Area:
_____________
Perimeter:
_____________
Type:
____________
C
a
C
j Math-Aids.Com
Name:Date:
5.2 The Area of a Triangle
Develop and apply the formula for the area of a triangle.
1. Calculate the area of each triangle.
a)
b)
6m
Complete the table.
Base Height Area of Triangle
a) 6cm 12cm
b) 8mm 32mm2
c) 120m 1200m2
d) 14.2 cm 12.3cm
At-Home I HelpYou can think of a triangle as
being half a rectangle or a
parallelogram.
For example, the shaded triangle
below is half the size of a
rectangle with the same height
and base.
5cm%%j
10cm
The area of a triangle is half the
area of a rectangle or
parallelogram with the same
height and base.
Area of a triangle:
A = (b x h) ÷ 2
3. Calculate the area of each shape.
A 4cm
B
a) triangle ABE
b) triangle ECD
c) triangle BEC
)
7 cm
E 2cm
F C
46 Chapter 5: MeasurementCopyright 0 2008 by Nelson Education Ltd.
N
Circle Geometry
Parts of a Circle
circumference: the distance around the outside of a circle. Itis similar to perimeter in rectangles, triangles and parallelograms.
diameter: a line segment that joins two points along thecircumference of a circle, and passes through the center. Youcould also call it the line that cuts a circle exactly in half.
radius: half of the diameter. it is a line drawn from the centerof a circle to any point around its circumference.
pi (it): the ratio of the circumference of a circle to itsdiameter.
• If you were to take a string and make it the exact length ofa circle’s diameter, how many lengths would it take to goaround the outside (circumference) of that circle?
• In every case, the answer is 3.14 times. This means thatthe circumference of a circle is equal to 3.14 times thediameter of the same circle.
• The number 3.14 is a constant which is true for all circlesand is given the name p1 and the symbol it.
• To find the circumference of any circle if you know thediameter, you may use the formula circumference is equal toTF times the diameter, or
• This formula may be rearranged to find the diameter if youalready know the circumference
Name:
If the diameter of a circle is 12 cm, what is the radius?
Formulas you may use:
You may use your yellow formula sheet
Label all of the parts of the circle:
radius, diameter, circumference,
If the radius of a circle is 7 cm, what is the diameter?
What number to we use to represent p1(11)?
What is the relationship between the diameter of the circle and thecircumference?
What is the relationship between the radius of a circle and the area of acircle?
Circumference
What is the circumference of the following circles?
Show all work - including the formula
LZET Lc=1 LZ1
Name:
Teacher
Score:
Date:
Identify the elements for each problem.
Circle:
__________
Radius:
__________
Diameter:
_________
P
Circle:
__________
Radius:
__________
Diameter:
_________
Circle:
Radius:
Diameter:
Circle:
__________
Radius:
__________
Diameter:
_________
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Diameter: VL.
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Circle:
Radius:
Diameter
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9)
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Radius:
Diameter:
G
Li Math-AidsCom
Name:
Teacher
Score:
Date:)
Solve the missing elements for each problem. Use 3.14 for P1.
Radius:
Diameter:
Circumference:
Area:
Radius:
Diameter:
Circumference:
Area:
F
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Radius:
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Diameter: 14 cm
Circumference:
Area:
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Area:
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Name:
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Score:
F—
Example:
Areaofacircle=nr2
Radius Cr) = 4 ft-
Area =nr2
=nx4x4
Area=16,Tft1
-
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Find the exact area of each circle.1)
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4)
Area=
5)
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6)
Area= ( :
7)
Area=
8)
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9)
Area= ( )
Area= Area= Area= ( )
3)
Printable Math Worksheets @ www.mathworksheets4kids.com
Name:
Ccircle - AreaD
Score:
,
\Example:Area of a circle = nr2
Dia meter =44 ftRadius (r) = 21.5 ft
Area = nr2
= 3.14x21.5 x21.5
Area= 1451.47 ft2—
—
Find the area of each circle. Round the answer to two decimal places. (use n =314)
2)
Area= :
Area= ( )
Area= )
3)
Area=
1)
4)
7)
Area= ‘1
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Printable Math Worksheets @ www.mathworksheets4kids.com
Name
(Circle - Are’J
Score:
—\
Example:Area of a circle = nr2
Radius Cr> 2.75 ft
Area = nr’
= 3.14 x 2.75 x 2.75
Area = 23.75 ft2
‘- .-
Find the area of each circle. Round the answer to two decimal places. ( use n = 3.14)
2)
4)
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5)
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6)
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Area= Area=
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Printable Math Worksheets @ www.mathworksheets4kids.com
Name:
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Score:
lift
Area =_______
Area =
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2ft
Area =_______
Area =
1i2in
Printa be Math Worksheets @ wwwmathworksheets4kidscom
Find the area of each figure.
1)
m
Area =
C
4)
Area =
3)
6)
9)
6 in
vi
3
2)
5)
8)
11)
Area = Area = Area =
7)
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Area =________ Area =
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6 yd
Area =________
Name:
___________________
Find the area of each figure.
C AnswerKey
Score:
Area = 36 in2 Area= 50m2
C
2 ft
Area= 20ft2
10)
Area =144n cm2
11)
Area= 121 ft2
12)
Area= 72m2
12 in
6 yd
Area= 78yd_ Area = 35 cm2 Area = 84 in2
Area= 55m2
1)
4)
7)
Area = 64n cm2
2)
5)
8)
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3)
6)
9)
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10 m
11 ft
Area j4_
Printabe Math Worksheets @ wwwmathworksheets4kidscom
Mixed Shapes
2 in
Area = Area =
Printabe Math Worksheets @ wwwmathworksheets4kidscom
Name: Score:
Find the area of each figure.
1)
3
Area =
12 m
Area =_______
m
61n
Area =
7 yd
2) 3)
4) 5) 6)
7) 8) 9)
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Area =
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Name:
Find the area of each figure.
1) 2)
CAnswer EJ
Score:,
3)
4)
Area = 36rr cm2
>‘
7 yd
5)
12 m
Area= 144m2
3
6)
6 in
Area= 84 in2
z
Area Area= 20hi2 Area = 81 m2
Area = 63 ft2 Area = lOOn m2 Area = 30 cm2
Printabe Math Worksheets @ wwwmathworksheets4kids.com
Area= 2iyd2
0
7)
10)
Area = 32 cm2
9m
Area= i6nft2
2 in5 yd
8)
11)
9)
12)
C’
7ft cm
Grade 7 Math — Measurement Review
Find Area
Find Area
Find Area
3r
J(OCjY.i
Find Area
Find Circumference
Grade 7 Math — Measurement Review
AREA of Shapes
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6cm 5cm
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