how to find
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Created BY:
Ryan Massey
How to Find …
Created by
Ryan Massey
RCM
What is Area?
Area is the “space” that is defined by the “pe(rim)eter”.
All shapes that are “2-d” or “two-dimensional” have Area.
The Orange In this shape
Is AREA
On the Next page we willLearn…
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How do I Find Area?
Do you know how to Find the AREA of..– Squares & Rectangles?– Triangles?– Circles?
If not, that’s a-ok, I’ll tell how on the next page
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Some of The “2-D” Area Formula’s
Shape(s) Formula(s) ~~~~~~Example~~~~~~
Square /
Rectangle
bh = A(and another formula for the Square).
bh = A6 x 3 =A
18 =A
Triangle ½ (bh)= A
Or
½(bh)=A½(5 x 10) =A
½ (50) = A
25 =A
Circles
3 6
5
10A
bh
2
Ar 2 2
56.12
414.3
2)143(
Ar 2
2
A
A
A.
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Squares & Rectangles
A Square has all the same length on all sides. – The area Formula for the square is “ “
A Rectangle has 2 sets of parallel lines , and each set has their own length.
The area formula for the rectangle is “ “
Practice Problems are on the next page…
As 2
Abh
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Examples
Find the Area of the square above… then check your steps below…
1st - 2nd - (5)2 =A3rd - 52 = 5 x 5 = 25
5
As 2
6 10
Find the Area of the square above… then check your steps below…
1st - bh = A 2nd - (6)(10)=A3rd - 60 = A
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Practice Problems
5 7.5
A
3.95
B19
14 ½
C
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Problem A
5 7.5
Write out our formula..
(bh) = A
Fill in the numbers that we know..
(5 x 7.5) = A
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Problem A (cont.)
5 7.5
Multiply the numbers in the Parenthesis…
(5 x 7.5) = A
37.5 = A
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Problem B
3.95
Write out our formula..
(s)2 = A
Fill in the numbers that we know..
(3.95)2 = A
(3.95)2 = A
Square the number
(3.95)2 = 15.60 = A
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Problem C
19
14 ½
Write out our formula..
(bh) = A
Fill in the numbers that we know..
(19 x 14.5) = A
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Problem C (cont.)
Multiply the numbers in the Parenthesis…
(19 x 14.5) = A
275.5 = A
19
14 ½
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Our Area's are…
5 7.5
37.5 = A
A
3.95
(3.95)2 = 15.60 = A
B
275.5 = A
19
14 ½ C
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Triangles
If you take a Square or rectangle, and place a Triangle on top of it, the area around the triangle would equal the area that was IN the triangle. ( give it a try).
HINT: Make sure you
½ the area after you have multiplied the Base (b) & Height (h) out.
Formula: ½(bh) = A or “ “.
The Base is the bottom of the triangle.
The Height is the Highest point of the triangle to the base… (look at the diagram on the
next page for more help).
Abh
2
)(
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Triangles (cont.)
The BLUE line is The Height of this
Triangle.
The RED Line is The Base of this
Triangle.
The GREEN Is the AREA
Of thisTriangle
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Practice Problems with Triangles
24
12
10
5
19
4
A BC
Created BY:
Ryan Massey
(suggestions)
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Problem A
24
12
AWrite out our formula..
½(bh) = A
Fill in the numbers that we know..
½(12 x 24) = AClick to See the
Next set ofSteps.
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Problem A (cont.)
24
12
A Multiply the numbers in the Parenthesis…
½(12 x 24) = A ½ (288) = A
Divide our area that we multiplied out by 2 or ½ .
½(288) = A ½(288) = 144
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Problem B
10
5
BWrite out our formula..
½(bh) = A
Fill in the numbers that we know..
½( 5 x 10) = AClick to See the
Next set ofSteps.
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Problem B (cont.)
Multiply the numbers in the Parenthesis…
½(5 x 10) = A ½ (50) = A10
5
B
Divide our area that we multiplied out by 2 or ½ .
½(50) = A ½(50) = 25
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Problem C
19
4
CWrite out our formula..
½(bh) = A
Fill in the numbers that we know..
½(4 x 19) = A
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Problem C (cont.)
19
4
CMultiply the numbers in the Parenthesis…
½(4 x 19) = A ½ (76) = A
Divide our area that we multiplied out by 2 or ½ .
½(76) = A ½(76) = 38
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A= 25
So… Our correct answers are..
24
12
A A= 144
10
5
B
19
4
CA = 38
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Circles
The Formulas for the circle are…
C , or circumference is the perimeter of the circle.
A or Area is the space that is inside or space that is in the circle.
Pi – is a number that is a VERY Long Number.
pi7
22 (appox.) 3.14
2rA
r2C
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Quick Definitions
Name/ Hint Definition
Radius ( or ) radii ( In red>>)
The line that is ½ of the distance of the Diameter
Diameter (in blue)
Is double of the radius.( Or )The line that goes from one side of the circle to the other side, passing through the center of the circle.
H
I
N
T
When the circle chows the Diameter, you still need to 1st find the radius. And square the radius. ( Or your answer will be WRONG!)
Radius
Diameter
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How do I find Area of a Circle?
2
Write out our formula..
Fill in the numbers that we know..
A= (3.14)(2)2
2rA
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Finding the Area of Circles (cont.)
Multiply the Numbers in the Parenthesis
Now, it is 6.28 to the 2nd power.
A= (3.14)(2)2 A= 6.282
A= 6.282 A= 39.43
2
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Practice Problems
5
8.5
30Find the AREA
Of the circles A-C
a
b
c
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Problem a
5
Write out our formula..
Fill in the numbers that we know..
A= (3.14)(5)2
2rA
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Problem a (cont.)
Multiply the Numbers in the Parenthesis
Now, it is 15.7 to the 2nd power.
A= (3.14)(5)2 A= 15.72
A= 15.72 A= 246.49
5
RCM
Problem b
30
Write out our formula..
Fill in the numbers that we know..
A= (3.14)(30)2
2rA
We Need to now find The RADIUS of this Circle.
30/2 = 15 <<15, is now The radii or radius for This problem.
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Problem b (cont.)
Multiply the Numbers in the Parenthesis
Now, it is 47.1 to the 2nd power.
A= (3.14)(15)2 A=47.12
A= 47.12 A= 2218.41
30
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Problem c
8.5
Write out our formula..
Fill in the numbers that we know..
A= (3.14)(8.5)2
2rA
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Problem c (cont.)
Multiply the Numbers in the Parenthesis
Now, it is 26.69 to the 2nd power.
A= (3.14)(8.5)2 A= 26.692
A= 26.692 A= 712.35
8.5
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So… Our Area’s are…
A= 246.49 5
A= 2218.41
30
A= 712.358.5
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