Question

find the length of each side of a regular hexagon whose area is 216 root 3 sq cm​

Answer 1

Required Answer:-

There are several methods for area of a regular hexagon but since we have to calculate the side by the provided area of the hexagon in the question,

We will use the formula:

$\large{ \boxed{ \rm{a = \dfrac{3 \sqrt{3} \: {side}^{2} }{2} }}}$

Putting the value of area to get the side,

⇒ 3√3 × side ² / 2 = 216√3 cm²

⇒ side² = 216√3 × 2 / 3√3 cm²

⇒ side² = 72 × 2 cm²

⇒ side ² = 144 cm²

⇒ side = 12 cm

Therefore:-

• The side of the regular hexagon is 12 cm.

• Note that: We can use different formulas like based on perimeter or 6 × area of each triangles depending on the question.

Answer 2

$\large \sf\underline{ \underline{ \red{solution : }}} \: \:$

$\boxed{ \tt{area \: of \: hexagon = \frac{3 \sqrt{3 } \: \: {x}^{2} }{2} }}$

Here ,

• 'x' is side of hexagon.

Area is 216√3cm².

$\\ \\ \implies \tt{216 \cancel{ \sqrt{ 3}} = \frac{3 \cancel{ \sqrt{3}} {x}^{2} }{2} } \\ \\ \ \\ \implies \tt{216 \times 2 = 3 {x }^{2} } \\ \\ \\ \implies\tt{432 = 3 {x}^{2} } \\ \\ \\ \implies \tt{ {x}^{2} = \frac{432}{3} } \\ \\ \\ \implies\tt{ {x}^{2} = 144 } \\ \\ \\ \underline{ \boxed {\tt{ \pink{x = 12cm }}}}$

Therefore , side of regular hexagon is 12cm.

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NOTE :-

• We can also use other formula according to question. In this question, we were given total area and we have to find the side , so we used this formula.

Area of hexagon = 6 × triangle