Upload
preston-henderson
View
223
Download
0
Tags:
Embed Size (px)
Citation preview
CCS:6.G.1. Find the area of right
triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems
Students will be able to:Find the areas of parallelograms, triangles, and circles
Find the circumference of circles
Find the area of complex figures
Objectives
…thus, changing it to a rectangle.What is the area of the rectangle?
AREA OF PARALLELOGRAM
h
b
lwA wlA lwA 2
AREA OF A PARALLELOGRAM
Since the area of the rectangle and parallelogram are the same, just rearranged, what is the formula for the area of this parallelogram?
h
b
bhA hbA bhA 2
Area of a Parallelogram
Any side of a parallelogram can be considered a base. The height of a parallelogram is the perpendicular distance between opposite bases.
The area formula is A=bh
A=bhA=5(3)A=15m2
Area of a parallelogram
Video Time
AREA OF A TRIANGLE
b
?
?
Remember, we divided the height into two equal parts.
Now take the top and rotate…
AREA OF A TRIANGLE
??
b…until you have a parallelogram.How would you represent the height of this parallelogram?
h2 h21h
AREA OF A TRIANGLE
The area of this triangle would be the same as the parallelogram. Therefore, the formula for the area of a triangle is… what?
h
b
bhA bhA 21 bhA 2
Finding the area of triangles
Video Time
The circumference of a circle is
The distance around a circle
Hint: Circumference remember circle around
Now Let’s Talk Circles….
People knew that the circumference is about 3 times the diameter but they wanted to find out exactly.
C = ? x d
C ≈ 3 x dThis means APPROXIMATELY EQUAL TO
Early Attempts
Egyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x d
Archimedes, said C ≈3.1419 x d
Fibonacci. In 1220 A.D. said C≈3.1418xd
What is the value of the number that multiplies the
diameter to give the circumference????
An approximation to ππ≈3.1415926535897932384626433832795
02884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................forever….
CircumferenceRemember, circumference is the
distance around the circle.If you divide a circle’s circumference
by its diameter, you always get the same irrational number – pi (symbol: )
This is true of every circle.We estimate pi to be 3.14 or the
fraction 22/7.
The formula for the area of a circle is
We say:Area = pi times radius squared
Finding the Area of a Circle
Example 2
13 cm
If you are given a diameter, divide it in half to find the radius. 13 divided by 2 equals 6.5 cm.
A = r2
A = (3.14)(6.52)A = (3.14)(42.25)
A = 132.665 cm2
The Area and Perimeter of a CircleA circle is defined by its diameter or radius
Diameter
radi
us The perimeter or circumference of a circle is the distance around the outside
The area of a circle is the space inside it
The ratio of π (pi)
diameter
ncecircumfere
π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The circumference is found
using the formula
C=π d or C= 2πr (since d=2r)
The area is found using the formula
A=πr2
Finding circumferenceNaming the parts of a circleFinding the area of circles
Video Time
Complex FiguresUse the appropriate formula to find the area of each piece.
Add the areas together for the total area.
Example
| 27 cm |
10 cm
24 cm
Split the shape into a rectangle and triangle.
The rectangle is 24cm long and 10 cm wide.
The triangle has a base of 3 cm and a height of 10 cm.
Solution
RectangleA = lwA = 24(10)A = 240 cm2
TriangleA = ½ bhA = ½ (3)(10)A = ½ (30)A = 15 cm2
Total FigureA = A1 + A2
A = 240 + 15 = 255 cm2
Classwork:
Try This Area of Parallelograms Game- You have to be QUICK!!Try This Baseball Game that finds area of trianglesHomework: Reteaching/Practice 9.4 HO