Transcript MULTIPLYING DECIMALS - Florida Virtual School

Area of Polygons
SECTION 5.03
After completing this lesson, you will be able to say:
I can use composition and decomposition to
determine the area of polygons.
I can solve problems involving area of polygons
using composition and decomposition.
Quadrilateral
What is a Polygon?
a plane figure with at
least three straight sides
and angles
Polygons
Polygons can be classified as regular or irregular.
Regular polygon:
A polygon that has all congruent sides and angles.
Irregular polygon:
A polygon that does not have all congruent sides
and angles
Examples of Polygons
Regular Polygons
How can we decompose this hexagon to find the area?
The key to decomposing and composing polygons is to use only shapes you are
familiar with. You would not want to decompose this hexagon into a shape you
do not have the dimensions for or that you do not know how to solve for the area
of.
Regular Polygons
Method 1
To find the area using the decomposition of 12 congruent triangles, all you need to do
is find the area of one of the right triangles and then multiply that by 12. Notice that the
base of the triangle will be 5 inches because the triangle’s base is half of the hexagon’s
side length.
Regular Polygons
Method 2
Try It!
• Can you use the deconstruction method to
find the area of this octagon?
Check your work
Irregular Polygons
How can we use decomposition to find the area of this irregular polygon?
Irregular Polygons
• Keep in mind there may be more than one way
you can decompose an irregular polygon
• Here are two examples of how we can
deconstruct this irregular polygon
Irregular Polygons
To calculate the area of this irregular
polygon, all you need to do is calculate the
area of each rectangle, then calculate the
sum of the areas.
Recall, the area of a rectangle A = l x w
Area of smaller rectangle
5 cm × 3 cm = 15 cm2
Area of larger rectangle
10 cm × 6 cm = 60 cm2
Total area of irregular polygon
15 cm2 + 60 cm2 = 75 cm2
Irregular Polygon
See if you can determine how to
decompose this shape
Irregular Polygons
You can see this irregular polygon is composed of one triangle and one
rectangle.
The triangle has a base of 10 cm and a height of 3 cm. The height of the
triangle was found by subtracting 9 from 12.
The rectangle has a length of 9 cm and a width of 8 cm.
Irregular Polygons
Try It!
Can you Calculate the area of the irregular polygon
shown below.
Check your work
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 polygons.
I can solve problems involving area of polygons
using composition and decomposition.