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GeometryQuestion and Answers: Page 3

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Calculate the area of the green shaded portions

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{green}\:\mathrm{shaded}\:\mathrm{portions} \\ $$

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The figure below represents a design on the windows of a building. The curved part XY is an arc of a circle. The rise of the segmental arc is 10cm, its span is 100cm and XZ=ZY=120cm. calculate: (i) the radius of the circle (ii) the area of the segmental cap, correct to 2 significant figures. (iii) the total area of the design, correct to 3 significant figures.

$${The}\:{figure}\:{below}\:{represents}\:{a}\:{design} \\ $$$${on}\:{the}\:{windows}\:{of}\:{a}\:{building}.\:{The} \\ $$$${curved}\:{part}\:{XY}\:{is}\:{an}\:{arc}\:{of}\:{a}\:{circle}. \\ $$$${The}\:{rise}\:{of}\:{the}\:{segmental}\:{arc}\:{is}\:\mathrm{10}{cm}, \\ $$$${its}\:{span}\:{is}\:\mathrm{100}{cm}\:{and}\:{XZ}={ZY}=\mathrm{120}{cm}. \\ $$$${calculate}: \\ $$$$\left({i}\right)\:{the}\:{radius}\:{of}\:{the}\:{circle} \\ $$$$\left({ii}\right)\:{the}\:{area}\:{of}\:{the}\:{segmental}\:{cap}, \\ $$$${correct}\:{to}\:\mathrm{2}\:{significant}\:{figures}. \\ $$$$\left({iii}\right)\:{the}\:{total}\:{area}\:{of}\:{the}\:{design},\:{correct} \\ $$$${to}\:\mathrm{3}\:{significant}\:{figures}. \\ $$

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