what you will learn? formulas for finding the areas of rectangles, parallelograms, triangles,...
TRANSCRIPT
AREA
What you will learn?Formulas for finding the areas of rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, and circles by cutting apart and rearrangingthese figures.
AREA
Area is the amount of surface space that a flat object has.Area is reported in the amount of square units.
When you measure the amount of carpet to cover the floor of a room, you measure it in square units.
Would the area of your bedroom or the area of your house be greater?
You’re right! The area of your house is greater than the area of your bedroom.
Area = 15 square feet
Lets find the area of this surface if each square is equal to one foot.
Count the number of squares.
1 2
3
4 5 6 7 8
9 10 11 12 13 14
15
Count the number of squares to determine the area of
this surface. What is the
area?
The area is equal to 9 square units.
Try this one!
1
5
2
4
7
3
6
8 9
Rectangle
What is the area formula?
Area Formulas
b.h
SquareWhat other shape has 4 right
angles?
Area Formulas
Can we use the same area formula?
Yes
b.h
Practice!Rectangle
Square
10m
17m
14cm
Area Formulas
AnswersRectangle
Square
10m
17m
14cm
196 cm2
170 m2
Area Formulas
So then what happens if we cut a rectangle in half?
What shape is made?
Area Formulas
Triangle2 Triangles
So then what happens to the formula?
b.h
2
Practice!Triangle
5 ft
14 ft
Area Formulas
Answers
35 ft2Triangle5 ft
14 ft
Area Formulas
Summary so far...
bh
Area Formulas
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bh
Area Formulas
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bh
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bh bh
Area Formulas
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bh bh2
Area Formulas
ParallelogramLet’s look at a parallelogram.
Area Formulas
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?
Area Formulas
ParallelogramWhat happens if we move one part to the end?
Area Formulas
What will the area formula be now that it is a rectangle?
b.h
ParallelogramBe careful though! The
height has to be perpendicular from the
base, just like the side of a rectangle!
Area Formulas
b.h
RhombusThe rhombus is just a parallelogram with all equal sides! So it also
has bh for an area formula.
Area Formulas
b.h
Practice!Parallelogram
Rhombus
3 in
9 in
4 cm
2.7 cm
Area Formulas
Answers
10.8 cm2
27 in2Parallelogram
Rhombus
3 in
9 in
4 cm
2.7 cm
Area Formulas
Let’s try something new with the parallelogram.
Area Formulas
You can use two trapezoids to make a parallelogram.
Let’s try to figure out the formula since we now know the area formula for a parallelogram.
Trapezoid
Area Formulas
So we see that we are dividing the parallelogram in half. What will that do to the formula?
b.h
2
TrapezoidBut now there is a problem.
What is wrong with the base?
Area Formulas
b.h2
Trapezoid
By adding them together, we get the original base from the parallelogram.
So we need to account for the split base, by calling the top base, base 1 and the bottom base, base 2
Area Formulas
base 1
base 1 base 2
base 2
The heights are the same, so no problem there.
(b1+ b2) h2
Practice!Trapezoid
11 m
3 m
5 m
Area Formulas
Answers
35 m2Trapezoid
11 m
3 m
5 m
Area Formulas
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bh
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bh
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bh
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bh bh
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
So there is just one more left!
Let’s go back to the triangle.You know that by reflecting a triangle, you can make a kite.
Area Formulas
Kite
KiteNow we have to
determine the formula. What is
the area of a triangle formula again?
Area Formulas
KiteNow we have to determine the formula. What is the area of a triangle formula again?
bh2
Area Formulas
Fill in the blank. A kite is made up of __?__ triangles.
So it seems we should multiply the formula by 2.
Kite
bh2
*2 = bh
Area Formulas
Kite
Now we have a different problem.
What is the base and height of a kite?
The green line is called the symmetry line, and the red line is half the other diagonal.
bh2
. 2 = bh
Area Formulas
KiteLet’s use kite vocabulary instead to create our formula.
b = Symmetry Line
h = Half the Other Diagonal
Area Formulas
Symmetry Line * Half the Other Diagonal
Practice!Kite
2 ft
10 ft
Area Formulas
Answers
20 ft2Kite2 ft
10 ft
Area Formulas
Summary so far...
bh
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bh
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bh
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bh bh
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
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bh bh2
(b1 + b2)h2
Symmetry Line * Half the Other Diagonal
Final SummaryMake sure all your formulas are written
down!
bh bh2
(b1 + b2)h2
Symmetry Line * Half the Other Diagonal