Lesson 20 last semester, grade five
Polygonal region
Polygonal region
this is a
polygon
How to calculate its area?
10cm
15cm
5cm
Segmentation method:
The area of a polygon can be calculated by dividing it into several triangles or rectangles.
10cm
15cm
5cm
Segmentation method:
First, cut out the shape of a kite in the middle.
Divide into two equal triangles, a and B.
A b
10cm
15cm
5cm
A b
5cm
15cm
Area of triangle a:
(
15 x 2
2
)
Square centimeter
= 15 cm2
Harrier area (A+B):
15 cm2 x 2
= 30 square centimeters
this is a
polygon
How big is its area?
16m
10 meter
6m
8m
6m
16m
Supplementary method:
Add a D figure to the white part of the original figure.
10 meter
6m
8m
6m
D
16m
Rectangular area:
10 meter
6m
8m
6m
(16 x 24) square meters
= 384 square meters
Area of part d:
(8 x 6) square meters
= 48 square meters
D
16m
Total area:
10 meter
6m
8m
6m
D
= (384-48) square meters
= 336 square meters
Rectangular region -D
Is there any other way to calculate the area of this graph?
16m
10 meter
6m
8m
6m
16m
Segmentation method:
10 meter
6m
8m
6m
C
Yes! can use
First, divide the graph into three rectangles: a, b, c, b, c.
A
B
Total area:
= 336 square meters
A = ( 10 x 16) m2
=160m2
16m
10 meter
6m
8m
6m
C
A
B
B = (8 x 10) m2.
= 80 square meters
C = (6 x 16) square meters
= 96 square meters
(160+80+96) m2
Use your head, how to find the area of this polygon?
Supplementary method
Segmentation method
4m
6m
12m
14 meter
It is better to calculate this figure by subsection method.
Is there any other way?
4m
6m
12m
14 meter
How to divide this number?
Please think about it!
Yes!
By segmentation
4m
6m
12m
14 meter
Segmentation method
2.a is a triangle and B is a trapezoid.
1. First, divide this polygon into two parts: A and B.
4m
6m
12m
14 meter
Steps:
A
B
Area of trapezoid b:
4m
6m
12m
14 meter
A
B
(
14 x 4
2
)
The second part of money supply
= 28 square meters
Area of triangle a:
(
( 12 + 18) x 14
2
)
The second part of money supply
= 2 10 m2
calculate
Sum of area of a
Area of b:
The sum of the areas of a and b is the area of this polygon.
4m
6m
12m
14 meter
A
B
(28+2 10) square meters
= 238 square meters
4m
6m
12m
14 meter
A is a triangle, b is a rectangle and c is a triangle.
It can be divided into three parts: a, b, c, b and C.
There is more than one way to divide a regular polygon! Can you think of other segmentation methods?
A
B
C
A+B+C = the total area of the polygon.
Method 1:
4m
6m
12m
14 meter
A, b and c are all triangles.
It can be divided into three parts: a, b, c, b and C.
A
B
C
A+B+C = the total area of the polygon.
Method 2:
8 cm
4 cm
What is the area of the polygon in the picture?
Please work it out.
The first part of the question:
4 cm
8 cm
4 cm
4 cm
It is better to calculate the polygons in the figure by segmentation method.
Divide the polygon into two identical parallelograms (A and B).
A
B
(A+B) = the total area of the polygon.
15m
12m
What is the area of the polygon in Figure m2?
Please work it out.
Question part (2):
8m
9m
15m
12m
8m
9m
Polygon b in the figure is better calculated by complement method.
Add a triangle A to the polygon in the diagram.
(rectangular area -A) = the total area of the polygon.
A
In this way, the polygon becomes a rectangle.
Are you interested in calculating the area of these polygons?
You are learning very well, please keep up your efforts!