area of a parallelogram
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Today we are going to find the Area of Parallelograms and
the Area of Triangles
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AreaThe number of square units that are needed to cover the surface of a figure.
PolygonAny straight-sided closed plane figure.
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Circle the polygons below.
Regular Polygon Polygon with all sides congruent and all angles congruent.
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Polygons Regular PolygonsName# of sides Picture NamePicture
3 Triangle AcuteEquilateral
4 Quadrilateral Square
5 Pentagon RegularPentagon
6 Hexagon RegularHexagon
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Polygons Regular PolygonsName# of sides Picture NamePicture
8 Octagon RegularOctagon
10 Decagon RegularDecagon
7 Heptagon
9 Nonagon
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The area of a rectangle is equal to the base times the height. Also known as length times width.
height
base
(h)
(b)
A =bh
A = bh is the same as A = lw
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What is the area of the rectangle?
2 in.
6 in.
26x
12 in.2
12 in2 or square inches
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A square is a special rectangle.Since the base and the height are the same size, we call them sides (s) instead of base and height.
sheight = s s
base = s
A= s2
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What is the area of the square?
4 m.
4 m.
44x
16 m.2
16 m2 or square meters
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Given the formula for area of a rectangle, we are
going to use that information to derive the formula for the area of a parallelogramWatch carefully not to
miss it!
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Draw a straight line from the top corner perpendicular to the base
Cut that triangle and move it to the other sideWhat
shape does it make?
Rectangle
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What is the formula for area of a parallelogram?
Use this information to find the area of a parallelogram
A parallelogram has the same area as a rectangle!
h
base = b
height = h h
b
A=b h
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4 cm.90º
2 cm.
= 8 cm.2
Check to see if you got it right.
A=b h
A=4 2
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Cut off the piece at the dotted line.
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Cut off the piece at the dotted line.
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Move this piece to the other side.
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Move this piece to the other side.
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Now you have a rectangle
A = 8 square cm. or 8 cm.2
Let’s check it with the area of a rectangle.
How many squares do you see?
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What is the area of this parallelogram?
7 cm.
5 cm. 57x
35 cm.2
35 square centimeters or 35 cm.2
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What is the area of this parallelogram?
6 ft.
5 ft.56x
30 ft.2
30 square feet or 30 ft.2
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Given the formula for area of a rectangle, we are going to use that information to
discover the formula for the area of a triangle.
Watch carefully not to miss it!
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Given a right triangle
Make a similar triangle,
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Given a right triangle
Make a similar triangle, flip it and put both triangles next to each other
What polygon is this?
A Rectangle
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What is the formula for the area of a triangle?
We can use the formula for area of a rectangle to find the formula for area of a triangle.
bA=2hA=b h
Two triangles make one rectangle.
We want to find half of the area of the rectangle.
We since we arefinding of the area.
÷2half
base
height
b
h
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When we put 2 right triangles together is made a rectangle.Watch what happens when instead we use 2 isosceles triangles.
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Given an isosceles triangle
Make a similar triangle,
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Given an isosceles triangle
Make a similar triangle, flip it and put both triangles next to each other
What polygon is this?
A Parallelogram
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base
height h
How do you find the area of the parallelogram?
Notice when we put two right triangles togetherit made a . When we put two isosceles triangles together it made a . We are still finding the area so we .half
rectangleparallelogr
dividea
by 2m
A= 12
bhbhA=2
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9 cm
5 cm 6 cm3 cm
A= 12
bhbhA=2
1A b h2
1A 9 32
1A 272
2A 13.5 cm
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The End!Take out your study guide!
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Area of a Parallelogram
# 3
5 in
3 in A = b x hA = 5 x 3 = 15 in2
To find the area for a parallelogram use what you know about area of a rectangle.
A = base x height
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# 4 Area of a Triangle
8 m
6 m
A = 8 x 62
= 24 m2
A = base x height 2
A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half.
1A= bh2
bhA=2
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