Search problems

1 problem matches “area of composite regions”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Area under a rotating rectangle's path ●●●○○ 50 ptsA $2 \times 3$ rectangle has vertices $(0,0)$, $(2,0)$, $(0,3)$, $(2,3)$. Rotate it $90^{\circ}$ clockwise about $(2,0)$, then $90^{\circ}$ clockwise about $(5,0)$, then $90^{\circ}$ clockwise about $(7,0)$, and finally $90^{\circ}$ clockwise about $(10,0)$, so that the side originally on the $x$-axis is back on the $x$-axis. A point of the rectangle initially at $(1,1)$ traces a curve during these rotations. Find the area of the region below this curve and above the $x$-axis. Round to two decimal places.