Question

1. Find the area of an equilateral triangle whose
each side is
(a) 30 cm
Please Give detailed answer I am not able to understand.​

Answer 1

Given: Each side of an equilateral triangle is 30 cm.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

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$\star\:\boxed{\sf{\pink{Area \: of \: equilateral \: \triangle = \dfrac{\sqrt{3}}{\:4} (a)^2 \ cm}}}$

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• Here, a is each side of the equilateral triangle.

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Therefore,

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$:\implies\sf Area_{\:\triangle} = \dfrac{\sqrt{3}}{2} \times \Big(30 \Big)^2 \\\\\\:\implies\sf Area_{\:\triangle} = \dfrac{\sqrt{3}}{2} \times 30 \times 30 \\\\\\:\implies{\underline{\boxed{\frak{\purple{Area_{\:\triangle} = 225\sqrt{3}\:cm^2}}}}}\:\bigstar$

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$\therefore\:{\underline{\sf{Hence, \ Area \ of \ equilateral \ \triangle \ is \ \bf{225 \sqrt{3} \ cm^2}.}}}$⠀⠀⠀

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Additional \: Information \: :}}}}}\mid}$

• Equilateral triangle is a triangle in which all the three sides have equal length.

• The sum of all three angles of an equilateral triangle is equal to 180°

• Altitude of equilateral triangle = $\sf\dfrac{\sqrt{3}a}{2}$

• Perimeter of equilateral triangle = Sum of all sides. (a + a + a) = 3a

Answer 2

Answer:

Given :-

• An equilateral triangle whose each side is 30 cm.

To Find :-

• What is the area of an equilateral triangle.

Formula Used :-

${\purple{\boxed{\small{\bold{Area\: of\: equilateral\: triangle\: =\: \dfrac{\sqrt{3}}{4}{(side)}^{2}\: cm}}}}}$

Solution :-

Given :

• Side = 30 cm

According to the question by using the formula we get,

⇒ $\sf Area\: =\: \dfrac{\sqrt{3}}{4} \times {(30)}^{2}\: cm$

⇒ $\sf Area\: =\: \dfrac{\sqrt{3}}{4} \times 30\: cm \times 30\: cm$

⇒ $\sf Area\: =\: \dfrac{\sqrt{3}}{4} \times 900\: c{m}^{2}$

⇒ $\sf Area\: =\: \dfrac{\sqrt{3}}{\cancel{4}} \times {\cancel{900}} c{m}^{2}$

⇒ $\sf Area\: =\: \sqrt{3} \times 225\: c{m}^{2}$

➠ $\sf\bold{\red{Area\: =\: 225\sqrt{3}\: c{m}^{2}}}$

$\therefore$ The area of an equilateral triangle is 225√3 cm².