1.

a board indicating "SWITCH OFF YOUR MOBILE" is of sides 5m , 6m and 9m . find its area using Heron's formula.​

Answer»

Before, finding the answer. Let's find out how we can find the answer.

  • In this QUESTION, we are asked to find the Area of the Triangular 'Switch off your MOBILE' BOARD by using Heron's formula.
  • So, to find the Area, we must first find the Semi-Perimeter for which the formula is :

\boxed{ \sf Semi-Perimeter = \dfrac{a + b +c }{2} }

  • Next, we must use the formula of :

\boxed{ \sf Area = \sqrt{s (s-a) (s-b) (s-c)} }

_______________________

Given :

  • Side 1 = 5 m
  • Side 2 = 6 m
  • Side 3 = 9 m

To find :

  • Area using Heron's formula

Solution :

{ \sf Semi-Perimeter = \dfrac{a + b +c }{2} }

                           \sf = \dfrac{5 + 6 + 9 }{2} }

                           \sf = \dfrac{20}{2} }

                            \sf = 10

{ \sf Area = \sqrt{s (s-a) (s-b) (s-c)} }

        \sf = \sqrt{10 (10-5) (10-6) (10-9)}

        \sf = \sqrt{10 \times (5) \times (4) \times (1)}

        \sf = \sqrt{50 \times 4}

        \sf = \sqrt{200}

THEREFORE, the Area of the Board is √200 m².


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