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6. In a circular table cover of radius 32 cm, adesign is formed leaving an equilateraltriangle ABC in the middle as shown inFig. 12.24. Find the area of the design. |
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Answer» Answer: mark as brainlist Step-by-step explanation: Radius of the circle = 32 cm Draw a MEDIAN AD of the TRIANGLE passing through the centre of the circle. Since, AD is the median of the triangle ∴ AO = Radius of the circle = 2/3 AD ⇒ 2/3 AD = 32 cm ⇒ AD = 48 cm In ΔADB, image By Pythagoras theorem, AB2 = AD2 + BD2 ⇒ AB2 = 482 + (AB/2)2 ⇒ AB2 = 2304 + AB2/4 ⇒ 3/4 (AB2) = 2304 ⇒ AB2 = 3072 ⇒ AB = 32√3 cm Area of ΔADB = √3/4 × (32√3)2 cm2 = 768√3 cm2 Area of circle = π R2 = 22/7 × 32 × 32 = 22528/7 cm2 Area of the design = Area of circle - Area of ΔADB = (22528/7 - 768√3) cm2 |
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