A book mark is shaped like a rectangle with a semicircle attached to at both ends. The rectangle is 12cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of the bookmark?

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08-02-2016
Mathematics

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A book mark is shaped like a rectangle with a semicircle attached to at both ends. The rectangle is 12cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of the bookmark?

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Leader Leader · Answer 1 · 2016-02-08T00:59:32+01:00

[tex]\sf\ The\ area\ of\ the\ bookmark\ is\ the\ area\ of\ the\ rectangle\ plus\ the\ area\ of\\the\ circle\ (two\ semi-circles\ make\ one\ circle).\\\\The\ area\ of\ the\ rectangle:\\12\times4=48\ cm\\\\The\ area\ of\ the\ two\ semicircles:\\\pi r^2=\\\pi 2^2=\\4\pi\ cm\\The\ width\ of\ the\ rectangle\ was\ the\ diameter\ of\ the\ cirlce.\ So\ the\ radius\\ was\ half\ the\ diameter\ or\ 2.\\\\The\ area\ of\ the\ bookmark:\\{\boxed{48\ cm+4\pi\ cm}[/tex]