A bookmark is like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm 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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A bookmark is like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm 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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Answer 1 · 2016-02-15T19:37:01

$(48 + 4 π) c m^{2} = 60.57 c m^{2}$ $(48 + 4pi) cm^2=60.57cm^2$

Explanation:

2 semicircles of equal diameters make one circle
$d i a m e t e r = 4$ $diameter=4$ => $r a d i u s = \frac{d i a m e t e r}{2} = 2$ $radius=(diameter)/2=2$

$S_{\circ} = π \cdot r^{2} = π \cdot 2^{2} = 4 π$ $S_circ=pi*r^2=pi*2^2=4pi$

$S_{rectangle} = length \cdot width = 12 \cdot 4 = 48$ $S_"rectangle"="length"*"width"=12*4=48$

$S_{T} = S_{rectangle} + S_{\circ} = (48 + 4 π) c m^{2} = 60.57 c m^{2}$ $S_T=S_"rectangle"+S_circ=(48 + 4pi) cm^2=60.57cm^2$

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

1 Answer

Explanation:

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