# Area of Circles, Sectors and Triangles

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What is the formula of the arc length of a sector in radians?
Arc length of a sector, s = rθ

What is the formula of the area of a sector in radians?
Area of a sector, A = 1/2r2θ

The following diagrams give the formulas for the arc length and area of a sector. Scroll down the page for more examples and solutions. Arc Length and Area of Sectors in radians

C2 Edexcel January 2013 Q7
7. The triangle XYZ in Figure 1 has XY = 6 cm, YZ = 9 cm, ZX = 4 cm and angle ZXY = α. The point W lies on the line XY.
The circular arc ZW, in Figure 1 is a major arc of the circle with centre X and radius 4 cm.
(a) Show that, to 3 significant figures, α= 2.22 radians.
(b) Find the area, in cm2, of the major sector XZWX.
The region enclosed by the major arc ZW of the circle and the lines WY and YZ is shown shaded in Figure 1.
Calculate
(c) the area of this shaded region,
(d) the perimeter ZWYZ of this shaded region.

Radians : C2 Edexcel January 2013 Q7(a)(b)

Area of Sector : C2 Edexcel January 2013 Q7(c)

Arc length : C2 Edexcel January 2013 Q7(d)

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