Page 142 - NUMINO TG_6A
P. 142
09Transforming It into a Parallelogram Unit
Objective: Learn how to find the area of a circle Use another method to estimate the area.
Divide the circle into 20 equal sectors.
This method will show how to estimate the area by rearranging parts of a circle into a parallelogram. Fit the 20 sectors together.
Now divide the same circle into 40 equal
Estimate the area of a circle using a different method. sectors.
Fit the 40 sectors together.
Divide the circle into 20 equal sectors. Observe to see whether the shapes
formed by 20 sectors or 40 sectors is
Place the 20 sectors as shown in the picture below. closer to a parallelogram.
40 sectors
To use the formula for the area of a parallelogram, divide the 20 sectors into
40 smaller sectors of equal size and shape. When you put the 40 sectors The figure made using the 40 sectors is
close to a parallelogram. The formula for
together, you will get a shape close to a parallelogram. finding the area of this figure can be derived
from the formula for the area of a
Which parallelogram is Radius parallelogram.
Area of a parallelogram
more accurate? (The
one with 40 sectors base height
because it has a
The base is the same length as half the
straighter edge.) circumference and the height is the radius.
Area of circle
Since the circumference Half the circumference = π radius
is equal to π diameter, (π radius 2) 2 radius
half the circumference is π radius radius
equal to π radius.
If you looking at the Area of circle = π radius radius
parallelogram
drawn, half the circumference
multiplied the radius is equal
to the area of the circle.
9. Transfoming It into a Parallelogram 75
Transforming a Circle into a Rectangle
When a circle is divided into 8, 16, and 32 parts and the parts are fitted together, it can be seen that the
figure is close to a parallelogram. The base of the figure is half of the circumference, so the area of the circle
can be found by multiplying (π radius) by the radius.
radius π radius
half the circumference (π radius 2) 2
radius radius
π radius π radius
6A Unit 09 125
Objective: Learn how to find the area of a circle Use another method to estimate the area.
Divide the circle into 20 equal sectors.
This method will show how to estimate the area by rearranging parts of a circle into a parallelogram. Fit the 20 sectors together.
Now divide the same circle into 40 equal
Estimate the area of a circle using a different method. sectors.
Fit the 40 sectors together.
Divide the circle into 20 equal sectors. Observe to see whether the shapes
formed by 20 sectors or 40 sectors is
Place the 20 sectors as shown in the picture below. closer to a parallelogram.
40 sectors
To use the formula for the area of a parallelogram, divide the 20 sectors into
40 smaller sectors of equal size and shape. When you put the 40 sectors The figure made using the 40 sectors is
close to a parallelogram. The formula for
together, you will get a shape close to a parallelogram. finding the area of this figure can be derived
from the formula for the area of a
Which parallelogram is Radius parallelogram.
Area of a parallelogram
more accurate? (The
one with 40 sectors base height
because it has a
The base is the same length as half the
straighter edge.) circumference and the height is the radius.
Area of circle
Since the circumference Half the circumference = π radius
is equal to π diameter, (π radius 2) 2 radius
half the circumference is π radius radius
equal to π radius.
If you looking at the Area of circle = π radius radius
parallelogram
drawn, half the circumference
multiplied the radius is equal
to the area of the circle.
9. Transfoming It into a Parallelogram 75
Transforming a Circle into a Rectangle
When a circle is divided into 8, 16, and 32 parts and the parts are fitted together, it can be seen that the
figure is close to a parallelogram. The base of the figure is half of the circumference, so the area of the circle
can be found by multiplying (π radius) by the radius.
radius π radius
half the circumference (π radius 2) 2
radius radius
π radius π radius
6A Unit 09 125
