Transcript Area of Quadrilaterals - Firelands Local Schools Home

Area of Quadrilaterals
Objectives
• I can find the areas of parallelograms,
rhombuses, and trapezoids.
Area of a Parallelogram
• What is a parallelogram?
• -a quadrilateral in which opposite sides are
parallel and congruent.
How do we find the area of a
parallelogram?
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In front of you is a parallelogram on the paper.
Cut it out
Cut your parallelogram along the dotted line.
Now move your triangular piece to the other
side of the parallelogram.
• What figure have you formed?
• Rectangle
• Does it have the same area as the
parallelogram?
• Base of the parallelogram is equal to
• The length of a rectangle
• The height of the parallelogram is equal to
• The width of a rectangle
Area of parallelogram continued
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Area of parallelogram is equal to
Area of rectangle
How do we find the area of a rectangle?
Area = product of the length and width
Area = length times width
A=(l)(w)
How do we find the area of a parallelogram?
Area = the product of the base and height
Area = base time height
A = bh
Find the area !
• The base of my parallelogram is 13 inches and the
height is 9 inches. Find the area.
• A = bh
• A = 13 · 9
• 117 inches squares
• Why are the units squared?
• We are multiplying and inch by an inch. This is no
different than multiplying 2 time 2 which can be
written as 2²
Math Talk
• On a piece of paper answer the following:
• How is the relationship between the length
and width of a rectangle similar to the
relationship between the base and height of a
parallelogram?
Trapezoid
• What is a trapezoid?
• A quadrilateral in which two sides are parallel.
Finding the area of a trapezoid
• Look at the two congruent trapezoids. What
do you notice?
• You should notice that the two trapezoids can
fit together to form a parallelogram.
• How does the trapezoid compare to the
parallelogram?
• It is half of it.
• If the trapezoid is half the parallelogram, then
the area of the trapezoid is?
• Half the parallelogram
• The height of the parallelogram is the same as
the height of the trapezoid. The base of the
parallelogram is the sum of the two bases of
the trapezoid.
• The Area of the trapezoid is found by adding
base 1 and base 2 and multiplying it by ½ the
height
• Area of a Trapezoid = 1/2h(b₁ +b₂)
Try some!
• A section of deck is in the shape of a
trapezoid, what is the area of this section of
deck if base one is 15 feet, base 2 is 25 feet
and the height is 21 feet.
• Area of a Trapezoid = 1/2h(b₁ +b₂)
• Area = ½ · 21 (15 + 25)
• 420 ft²
Math Talk
• On your piece of paper. Answer the following.
• Does it matter which of the trapezoids bases is
substituted for b₁ and which is substituted for
b₂? Why or Why not?
Rhombus
• A rhombus is a quadrilateral in which all sides
are congruent and opposite sides are parallel.
• Can a square be classified as a rhombus?
• Yes, all side are congruent and opposite side
are parallel.
• Some people call a rhombus a
• Diamond or a kite
• A diagonal is a line that can be drawn from
one vertices to the opposite vertices.
Area of a rhombus
• A rhombus can be divided into four triangles.
• Go ahead and cut your rhombus into 4
triangles.
• Rearrange them into another shape.
• Rectangle
• The base of the rectangle is the same length
as one of the diagonals of the rhombus. The
height of the rectangle is ½ the length of the
other diagonal.
Rhombus Formula
• The area of a rhombus is half of the product of
its two diagonals.
• A = 1/2·d₁ · d₂
Try one!
• Cedric is constructing a kite in the shape of a
rhombus. The spars (wood pieces that fabric
attaches to. These would be the diagonals) of
the kite measure 15 inches and 24 inches.
• How much fabric will Cedric need for the kite?
• A = 1/2d₁d₂
• A= ½ · 15 · 24
• A= 180 in²
Looking at the formulas
• What were all the formulas based upon?
• The parallelogram or rectangle.
Higher Order Thinking
• Answer the following:
• Simon says that to find the area of a trapezoid,
you can multiply the height by the top base
and by the bottom base, then add the two
products together and divide the sum by 2. Is
Simon correct? Explain your answer.
Advanced Multistep
• The height of a trapezoid is 8 in. and its area is
96 in². One base of the trapezoid is 6 inches
longer than the other base. What are the
lengths of the bases. Explain how you found
your answer.
Multistep
• The height of a trapezoid is 8 in. and its area is
96 in². One base of the trapezoid is 6 inches
long. What is the length of the other base.
Explain how you found your answer.
Practice