What is the Remaining Portion of the Area? If

In an equilateral triangle of side 24 m, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is ( √3 = 1.732)

  1. 98.688 sq cm
  2. 100 sq cm
  3. 101 sq cm
  4. 95 sq cm
Manish Listener Asked on 17th July 2015 in No Category.
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    Answer: (1) 98.688 cm2

    Explanation:-
    Formula-
    The area of the equilateral triangle = sqrt.3 x a2/4
    Given-
    In the figure –

    RE: What is the Remaining Portion of the Area? If


    Side of equilateral triangle = 24 cm
    Then, the area of the equilateral triangle = sqrt.3 x 24 x 24/4
    = 1.732 x 6 x 24                       (sqrt.3 = 1.732)
    = 249.408 cm2
    In triangle OLQ,
    tan 30o = OL/LQ
    1/sqrt.3 = r/12
    r = 12/sqrt.3
    r = 12 sqrt.3/3
    r = 4 sqrt.3
    Formula-
    The area of the circle = pie x r2
    = 3.14 x (4 sqrt.3)2
    = 3.14 x 16 x 3
    = 150.72 cm2
    The area of the remaining part = The area of the equilateral triangle PQR – The area of the circle
    = 249.408 – 150.72
    = 98.688 cm2

    Hence, the answer is (1) 98.688 cm2.

    Anurag Mishra Professor Answered on 17th July 2015.
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