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Area FormulasArea Formulas
Rectangle
Rectangle
What is the area formula?
Rectangle
What is the area formula? bh
Rectangle
What is the area formula? bh
What other shape has 4 right angles?
Rectangle
What is the area formula? bh
What other shape has 4 right angles?
Square!
Rectangle
What is the area formula? bh
What other shape has 4 right angles?
Square!
Can we use the same
area formula?
Rectangle
What is the area formula? bh
What other shape has 4 right angles?
Square!
Can we use the same
area formula? Yes
Practice!Practice!Rectangle
Square
10m
17m
14cm
AnswersAnswersRectangle
Square
10m
17m
14cm
196 cm2
170 m2
So then what happens if we cut a rectangle in half?
What shape is made?
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?2 Triangles
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?2 Triangles
So then what happens to the formula?
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?2 Triangles
So then what happens to the formula?
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?2 Triangles
So then what happens to the formula?
bh
TriangleSo then what happens if we
cut a rectangle in half?
What shape is made?2 Triangles
So then what happens to the formula?
bh2
Practice!Practice!Triangle
5 ft
14 ft
AnswersAnswers
35 ft2Triangle5 ft
14 ft
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh bh
Summary so Summary so far...far...
bh bh2
ParallelogramLet’s look at a parallelogram.
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?What will the area formula
be now that it is a rectangle?
ParallelogramLet’s look at a parallelogram.
What happens if we slice off the slanted parts on the
ends?What will the area formula
be now that it is a rectangle?
bh
ParallelogramBe careful though! The
height has to be perpendicular from the
base, just like the side of a rectangle!
bh
ParallelogramBe careful though! The
height has to be perpendicular from the
base, just like the side of a rectangle!
bh
ParallelogramBe careful though! The
height has to be perpendicular from the
base, just like the side of a rectangle!
bh
RhombusThe rhombus is just a parallelogram with all equal sides! So it also
has bh for an area formula.
bh
Practice!Practice!Parallelogram
Rhombus
3 in
9 in
4 cm
2.7 cm
AnswersAnswers
10.8 cm2
27 in2Parallelogram
Rhombus
3 in
9 in
4 cm
2.7 cm
Let’s try something new with the parallelogram.
Let’s try something new with the parallelogram.
Earlier, you saw that you could use two trapezoids to make a parallelogram.
Let’s try something new with the parallelogram.
Earlier, you saw that you could 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
Trapezoid
TrapezoidSo we see that
we are dividing the
parallelogram in half. What will that do to the formula?
TrapezoidSo we see that
we are dividing the
parallelogram in half. What will that do to the formula?
bh
TrapezoidSo we see that
we are dividing the
parallelogram in half. What will that do to the formula?
bh2
TrapezoidBut now there is a problem.
What is wrong with the base?
bh2
Trapezoid
bh2
So we need to account for the split base, by calling the top base,
base 1, and the bottom base, base 2. By
adding them together, we get the original base from the parallelogram.
The heights are the same, so no problem
there.
Trapezoid
(b1 + b2)h2
So we need to account for the split base, by calling the top base,
base 1, and the bottom base, base 2. By
adding them together, we get the original base from the parallelogram.
The heights are the same, so no problem
there.
base 2
base 1
base 1
base 2
Practice!Practice!Trapezoid
11 m
3 m
5 m
AnswersAnswers
35 m2Trapezoid
11 m
3 m
5 m
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh bh
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
So there is just one more left!
So there is just one more left!
Let’s go back to the triangle.
A few weeks ago you learned that by reflecting a triangle, you can make a kite.
KiteSo there is just one
more left!
Let’s go back to the triangle.
A few weeks ago you learned that by reflecting a triangle, you can make a kite.
KiteNow we have to
determine the formula. What is
the area of a triangle formula again?
KiteNow we have to
determine the formula. What is
the area of a triangle formula again?
bh2
KiteNow we have to
determine the formula. What is
the area of a triangle formula again?
bh2
Fill in the blank. A kite is made up of
____ triangles.
KiteNow we have to
determine the formula. What is
the area of a triangle formula again?
bh2
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
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
KiteLet’s use kite
vocabulary instead to create our formula.
Symmetry Line*Half the Other Diagonal
Practice!Practice!Kite
2 ft
10 ft
AnswersAnswers
20 ft2Kite2 ft
10 ft
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh
Summary so Summary so far...far...
bh bh
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Summary so Summary so far...far...
bh bh2
(b1 + b2)h2
Symmetry Line * Half the Other Diagonal
Final SummaryFinal SummaryMake sure all your formulas are written Make sure all your formulas are written
down!down!
bh bh2
(b1 + b2)h2
Symmetry Line * Half the Other Diagonal