Maths summer assignment
2014-08-09 11:14 pm
In the figure, OAB is a sector of radius r and arc length l, and △ CDE is a triangle of height r and base length l. Proce that the area of sector OAB is equal to the area of triangle CDE
回答 (2)
2014-08-10 8:14 pm
✔ 最佳答案
In sector OAB :Angle at centre, ∠AOB = 360° × (l/2πr) = (180l/πr)°
Area of sector OAB = πr² × [(180l/πr) / 360] = rl/2
Area of ΔCDE = (1/2) × l × r = rl/2
Hence, Area of sector OAB = Area of ΔCDE
參考: Adam
2014-08-10 3:37 am
Suppose O is the center of the circle
Consider the arc length,
2πr θ/360°=l ... where θ is ∠AOB
θ/360°=l /(2πr)
The area of sector OAB
=r²π (θ/360°)
=r²π l /(2πr)
=rl /2
The area of △CDE= rl /2
∴The area of sector OAB is equal to the area of triangle CDE
Consider the arc length,
2πr θ/360°=l ... where θ is ∠AOB
θ/360°=l /(2πr)
The area of sector OAB
=r²π (θ/360°)
=r²π l /(2πr)
=rl /2
The area of △CDE= rl /2
∴The area of sector OAB is equal to the area of triangle CDE
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