Consider the parabola sector defined by the chord AB. Draw the tangents at A, B and build triangle ABE. Show that the area of the parabolic sector is 2/3 of the area of ABE.
Use the fact that the line CD of middles of AE, BE is tangent to the chord (see ParabolaChords.html ) and area(EDC)=area(ABE)/4. Then use repeatedly a subdivision of the sector as shown to produce a series for the area of the sector and prove it to be 2a/3 (denoting by a=area(ABE)).
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Parbolic sector area ![[0_0]](ParabolaArea_files/ParabolaArea_0_0_0.png)
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![[1_0]](ParabolaArea_files/ParabolaArea_0_1_0.png)
![[1_1]](ParabolaArea_files/ParabolaArea_0_1_1.png)
![[0_0]](ParabolaArea_files/ParabolaArea_1_0_0.png)