1
four
The difference between the area of a circle and the area of a semicircle with a diameter of 4 cm can be solved by calculating the area formula of a circle.
Solution: Solution: 3. 14×42×
1
four
-3. 14×(4÷2)2÷2
= 12.56-6.28
=6.28 (square centimeter)
A: The shadow area is 6.28 square centimeters.
Comments: When calculating the area of irregular graphics, it is generally necessary to convert the area of irregular graphics into the sum or difference of the areas of several regular graphics.
Points: circles and composite shapes
Special topic: understanding and calculation of plane graphics
Analysis: The shaded area is the square area minus four blank areas, and the square area minus two semicircles is the area of two notches. The square area is 4×4= 16 cm2, and the two semicircles are 3. 14× (
four
2
) 2= 12.56 cm2.
Solution: Solution: The two blank areas are:
4×4-3. 14×(
four
2
)2
= 16- 12.56
=3.44 (square centimeter);
So the shaded part is:
4×4-3.44×2
= 16-6.88
=9. 12 (square centimeter);
A: The shadow area is 9. 12 cm2.
Comments: This problem can also be analyzed in this way: the sum of the areas of the four semicircles MINUS the area of the square is exactly equal to the area of the shadow part: 3. 14× (
four
2
) 2× 2-4× 4 = 25.12-16 = 9.12 (square centimeter
Divide the shadow into four areas of ABCD.
Take area a as an example. Region A is contained in two semicircles (upper semicircle and left semicircle respectively).
That is to say, when calculating the area of the upper semicircle and the left semicircle (that is, adding the areas), the area A is calculated twice.
By analogy, BCD has been calculated twice.
What are the square rows on the picture?
It's four semicircles. Four semicircles filled the square.
Is the sum of the areas of four semicircles.
And the shadow ABCD was added twice.
So square area = four semicircles area-shadow area
So shadow area = four semicircles area-square area.