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Standard X

Mathematics

Areas of Combination of Plane Figures

The figure is...

Question

The figure is made up of an isosceles triangle and a semi-circle. Find the perimeter of the figure.

2 (7 - 2 π) c m .

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(7 + 2 π) c m .

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2 (7 + 2 π) c m .

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(7 - 2 π) c m .

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Solution

The correct option is C $2 (7 + 2 π) c m .$
Perimeter of semicircular arc = $π \times \frac{d}{2}$
$= π \times \frac{8}{2}$
$= 4 π c m$

Total Perimeter = Perimeter of semi-circular arc $+$ Sum of outer sides of triangle $A B C$
Total Perimeter $= l (B O C) + C A + A B$
$= 7 + 7 + 4 π$
$= 14 + 4 π$
$= 2 (7 + 2 π)$ cm

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The figure is made up of an isosceles triangle and a semi-circle. Find the perimeter of the figure.

The correct option is C 2(7+2π)cm.Perimeter of semicircular arc = π×d2=π×82=4π cmTotal Perimeter = Perimeter of semi-circular arc + Sum of outer sides of triangle ABCTotal Perimeter =l(BOC)+CA+AB=7+7+4π=14+4π=2(7+2π) cm