Find the area of equilateral triangle with side a. Please answer with completely simplified exact values. Answer: A = sq. Units

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Find the area of equilateral triangle with side a. Please answer with completely simplified exact values. Answer: A = sq. Units

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2 months 2021-09-02T20:38:43+00:00 1 Answers 1 views 0

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    2021-09-02T20:40:25+00:00

    Solution :

    It is given that the length of a side of a triangle is given by ‘a’.

    It is an equilateral triangle.

    So the three sides will be of equal length and is a, a, a units.

    Now the semi perimeter of the equilateral triangle is given by :

    $S=\frac{a+a+a}{2}$

      $=\frac{3}{2}a$

    Therefore, using the Heron’s formula, we can find the area of the equilateral triangle.

    Area of the equilateral triangle is given by :

    $A =\sqrt{S(S-a)(S-a)(S-a)}$

    $A =\sqrt{\frac{3a}{2}\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)}$

    $A=\frac{\sqrt3}{4}a^2$ square units.

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