Editorial clarification: the supplied solution assumes that $E$ is the midpoint of $BC$, so

Question

Editorial clarification: the supplied solution assumes that $E$ is the midpoint of $BC$, so $CE=3\text{ cm}$. This is not stated or marked in the supplied diagram. Part (a) is determined without it; the answers to parts (b)–(e) below are conditional on this intended midpoint assumption.

In the figure, $ABCD$ is a square, where arcs $BD$, $EF$ are quadrants and arc $BC$ is a semicircle, such that $ABCD$ is fragmented into five regions. Let $①, ②, ③, ④$ and $⑤$ denote the area of each corresponding region. Find, leaving your answers in terms of $\pi$,

the area denoted by $②+⑤$,
the area denoted by $②+③$,
the ratio of the area denoted by $②+③$ to the area denoted by $④+⑤$,
the area denoted by $②-④$，
the area denoted by $①+③-⑤$.

Accepted Answer

Assuming E is the midpoint of BC for parts (b)–(e): (a) $\dfrac{9}{2}\pi\text{ cm}^2$ (b) $\dfrac{27}{4}\pi\text{ cm}^2$ (c) $3:1$ (d) $\dfrac{9}{4}\pi\text{ cm}^2$ (e) $\left(36-\dfrac{27}{4}\pi\right)\text{ cm}^2$

IP1U13 HOT Q2

IP1U13 HOT Q2

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