Mathegoras

Coordinate geometry › Polar and parametric curves › Areas in polar coordinates

Area swept by a bent segment

High school · ●●●○○ 50 pts

Plot points A,B,CA, B, C at coordinates (0,0)(0,0), (0,1)(0,1) and (1,1)(1,1) in the plane, respectively. Let SS denote the union of the two line segments ABAB and BCBC. Let X1X_{1} be the area swept out when Bobby rotates SS counterclockwise 45∘45^\circ about point AA. Let X2X_{2} be the area swept out when Calvin rotates SS clockwise 45∘45^\circ about point AA. Find X1+X22\frac{X_{1}+X_{2}}{2}. Round to two decimal places.

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rotationarea of sectorcircular sectors