Area of
Quadrilaterals
SECTION 5.02
After completing this lesson, you will be able
to say:
I can use composition and decomposition to
determine the area of quadrilaterals.
I can solve problems involving area of
quadrilaterals using composition and
decomposition.
Quadrilateral
What is a Quadrilateral?
Any 4 sided shape
Multiplying Decimals – words to know
Quadrilaterals
Can you name the quadrilateral?
Quadrilaterals - Parallelogram
A parallelogram is a four-sided polygon with two pairs of parallel and
congruent sides.
You can identify which sides are congruent because you will see
matching tick marks on them.
Quadrilaterals - Rhombus
The rhombus is a parallelogram where all the
sides are congruent.
A square is a special rhombus where all sides
are congruent and perpendicular.
Quadrilaterals - Kite
A kite has two pairs of congruent sides.
The important thing about the congruent
sides is that they are adjacent (or next) to
each other, not on opposite sides from each
other.
Quadrilateral - Trapezoid
A trapezoid is a quadrilateral in which one pair of opposite sides is
parallel.
You can see which sides are parallel because of the arrowhead.
These sides are called bases of the trapezoid. The other sides can be
of any length.
Quadrilaterals – Special Trapezoids
There are two special trapezoids
An isosceles trapezoid is a special
trapezoid where the nonparallel sides are
congruent.
A right trapezoid has a side that is
perpendicular to its parallel bases.
Area of Quadrilaterals
The area of quadrilaterals can be found by decomposing the shape into
rectangles and triangles. Recall the formulas for calculating the area for both
shapes.
Area of Parallelogram
How can we decompose this parallelogram into triangles
and rectangles?
Area of Parallelogram
A parallelogram can be decomposed into two right triangles with
a rectangle in between them. Drawing vertical lines from the
corners to the base will create a height for the side triangles and
a width for the rectangle. The important thing to notice is that the
two side triangles are congruent.
Area of Parallelogram
To calculate the area of the parallelogram,
add up the area of each shape created
from the decomposition.
Area of a Rhombus
How can we decompose this parallelogram into
triangles and rectangles?
Area of a Rhombus
One way to compose a rhombus is by
putting two congruent triangles together, so
its decomposition would be just that.
Area of a Rhombus
Triangle A:
The base is 8 inches, and the height is 4 inches.
1
A = 2bh
1
A=2 8 4
A=
1
2
32
A = 16 in2
Triangle B:
It will have the same area since it is congruent.
Area = triangle A + Triangle B
A = 16 + 16
A = 32 in2
Area of a Rhombus
• Is there another we can decompose the
Rhombus
Area of Rhombus
Notice in this decomposition, 4 congruent
right triangles were created. The area of
the rhombus is just 4 times the area of one
of the triangles.
This is just an example to show you there is
more than one way you can decompose a
shape into triangles and rectangles.
Area of a Kite
• How can we decompose the kite to find
the area?
Area of a Kite
A kite is composed of 4 right triangles.
Triangle A and B are congruent
Triangle C and D are congruent
So to find the area of the kite, you need to
just find the area of Triangle A and C, then
double it.
Area of a Kite
Triangle A:
The base is 6 ft., and the height is 7 ft.
Triangle C:
The base is 16 ft., and the height is 7 ft.
Remember, triangle A and B are congruent,
and triangle C and D are congruent.
Total Area = 2A + 2C
A = 2(21) + 2(56)
A = 42 + 112
A = 154 ft2
Area of a Right Trapezoid
• How can you decompose this Right
Trapezoid?
Area of a Right Trapezoid
Area of a Right Trapezoid
Triangle: The base is 2 m, and the height is 6.5 m.
Rectangle: The length is 6.5 m, and the width is 5 m.
Total area = Triangle + rectangle
A = 6.5 + 32.5
A = 39 m2
Area of an Acute Trapezoid
• Can you use the decomposition method to
find the area of this trapezoid?
Check your work
Apply It!
Can you apply what we have learned to solve this real world
problem?
Sam is building a kite for this weekend. He is headed to the craft store to buy
the materials. The material for the fabric is $0.30 for 10 square inches. How
much will the fabric cost to make the kite below?
Check your work
Now that you completed this lesson, you
should be able to say:
I can use composition and decomposition to
determine the area of quadrilaterals.
I can solve problems involving area of
quadrilaterals using composition and
decomposition.