Question

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

Answer 1

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.