Q. 363.8( 4 Votes )

# In an equilateral triangle of side 12cm, a circle is inscribed touching its sides. Find the area of the portion of the triangle not included in the circle. [Take √3=1.73 and π=3.14]

Answer :

Area of shaded region = Area of ΔABC – Area of circle

Given side of triangle = 12cm

= 36√3cm^{2}

Now, we have to find the area of a circle. For that we need a radius.

Draw AD ⊥ BC

So, In BDO

⇒ r = 2√3cm

Now, Area of circle = πr^{2}

= 3.14 × (2√3)^{2}

= 37.68cm^{2}

Area of shaded region = Area of ΔABC – Area of circle

= 36√3 – 37.68

= 36(1.73) – 37.68

= 24.6cm^{2}

Hence, the area of the portion of the triangle not included in the circle is 24.6cm^{2}

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PREVIOUSThe area of an equilateral triangle is 100√3cm2. Taking each vertex as centre, a circle is described with a radius equal to half the length of the side of the triangle, as shown in the figure. Find the area of that part of the triangle which is not included in the circles [Take π=3.14 and √3=1.732]NEXTIn a circular table-cover of radius 16cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the figure. Find the area of the design (shaded region in the figure).

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