Half arc length = ∏ d ÷ 2
=3. 14×4÷2
= 6.28 cm
The arc length of the sector is calculated by multiplying the circumference of the circle by the fraction (45-360) of the central angle of the sector.
2×3. 14×4×﹙45÷360﹚
=25. 12×45/360
= 3.14cm
The perimeter of the shaded part is 6.28+3.14+4 =13.42 cm.
From the point where the sector and semi-arc intersect with the sector radius to point B, you will find that there is an isosceles right triangle in the middle, and the upper right shadow part is equal to the upper left blank part. If the upper right shadow part is moved to the upper left blank, the area of the shadow part becomes a sector area with a central angle of 45 degrees minus the area of an isosceles right triangle. The base of a triangle is 4cm, and the height is the radius of a semicircle (4-2).
3. 14×4? ×﹙45÷360﹚-4×﹙4÷2﹚÷2
=50.24×45/360-4×2÷2
=6.28-4
=2.28cm？