In a figure, arcs are drawn …

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In a figure, arcs are drawn by taking vertices A,B and C of an equilateral triangle of side 10cm.as centres to intersect the sides BC,CA and AB at their respective mid-points D,E and F find the area of the shaded region... (use pai as 3.14)
  • 1 answers

Preeti Dabral 1 month, 1 week ago

Similar as(side=14cm): 

As per the given figure in question,
∠ABC = ∠BAC = ∠ACB = 60 ….[In an equilateral triangle all angles are of 60° each]
Now θ = 60°, r = {tex}{14 \over 2}{/tex} = 7 cm
Area of shaded region = ar(ΔABC) – 3{tex}\times{/tex} (area of minor sector)
{tex}{ = \frac{{\sqrt 3 }}{4}{{\left( {Side} \right)}^2}\; - \;3 \times \frac{\emptyset }{{360}}\;\pi {{\text{r}}^2}}{/tex}
{tex}{ = \;\;\frac{{1.73}}{4}\; \times 14 \times 14\; - \;3 \times \frac{{60}}{{360}}\; \times \;\frac{{22}}{7} \times 7 \times 7}{/tex}
{tex}{ = \;1.73\; \times 7 \times 7\; - \;3\; \times \frac{1}{6} \times 22 \times 7}{/tex}
{tex}{ = \;84.77\; - \;\frac{1}{2} \times 22 \times 7}{/tex}
{tex}{ = \;84.77\; - \;\;11 \times 7}{/tex}
= 84.77 - 77
= 7.77 cm2
Hence, the area of the shaded region = 7.77 cm2

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