Question

5. Using Heron's formula, find the area of an equilateral
triangle of side x cm.​

Answer 1

$\bf \huge {\underline {\underline \red{SoLuTiOn}}}$

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Answer

$\bf Area = \frac{ \sqrt{3} {x}^{2} }{4} {cm}^{2}$

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Given

• Side of triangle = x cm

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To Calculate

• Area of △ Using Heron's Formula

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Solution

A = x cm, B = x cm, C = x cm

Semi Perimeter = A + B + C / 2

= x + x + x / 2

= 3x / 2

Using Heron's Formula

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

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$\bf \implies \sqrt{ \frac{3x}{2}( \frac{3x}{2} - x) ( \frac{3x}{2} - x)( \frac{3x}{2} - x)}$

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$\bf \implies \sqrt{ \frac{3x}{2} \times \frac{1x}{2} \times \frac{1x}{2} \times \frac{1x}{2} }$

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$\bf \implies \sqrt{ \frac{ {3x}^{4} }{16} }$

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$\bf \implies \frac{ \sqrt{3 {x}^{4} } }{4}$

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$\bf \implies\frac{ \sqrt{3} {x}^{2} }{4} {cm}^{2}$

Answer 2

Answer:

Answer

\bf Area = \frac{ \sqrt{3} {x}^{2} }{4} {cm}^{2}Area=43x2cm2

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Given

Side of triangle = x cm

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To Calculate

Area of △ Using Heron's Formula

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Solution

A = x cm, B = x cm, C = x cm

Semi Perimeter = A + B + C / 2

= x + x + x / 2

= 3x / 2

Using Heron's Formula

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

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\bf \implies \sqrt{ \frac{3x}{2}( \frac{3x}{2} - x) ( \frac{3x}{2} - x)( \frac{3x}{2} - x)}⟹23x(23x−x)(23x−x)(23x−x)

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\bf \implies \sqrt{ \frac{3x}{2} \times \frac{1x}{2} \times \frac{1x}{2} \times \frac{1x}{2} }⟹23x×21x×21x×21x

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\bf \implies \sqrt{ \frac{ {3x}^{4} }{16} }⟹163x4

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\bf \implies \frac{ \sqrt{3 {x}^{4} } }{4}⟹43x4

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\bf \implies\frac{ \sqrt{3} {x}^{2} }{4} {cm}^{2}⟹43x2cm2