Question

. The Perimeter of an equilateral triangle is 60m. the area is

a) 10 √ sq.m b) 15 √ sq.m c) 20√sq.m d) 100√sq.m ​

Answer 1

Correct Question:-

• $\sf \: The \: Perimeter \: of \: an \: equilateral \: triangle \\ \sf \: is \: 60m. \: the \: area \: is$

$\bf \: a) 10 \sqrt{3} sq.m \\ \bf \: b) 15 \sqrt{3} sq.m \\ \bf \: c) 20 \sqrt{3} sq.m \\ \bf \: d) 100 \sqrt{3} sq.m$

Given:-

• Perimeter of equilateral triangle

To find:-

• The area of an equilateral triangle

Answer:-

• $100 \sqrt{3} m ^{3}$

Solution:-

Before finding the area we will first find the sides if equilateral triangle

We know that perimeter of equilateral triangle is:-

⇒3×side

$\large \sf \: ⇒3 \times sides = 60 \: cm$

$\large \: ⇒ \sf \: sides = \frac{60}{3}$

$\large \sf \: ⇒ \: sides \: = 20 \: cm$

Therefore the measure of sides is 20 cm.

$\large\boxed{ \underline{ \purple{ \sf{Area \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{4} \times sides ^{2} }}}}$

$\\ \: \: \: \: \: \: \: \: \: \: \sf \: = \frac{ \sqrt{3} }{4} \times 20 \times 20$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 \sqrt{3} {cm}^{2}$

$\large \dag \: { \boxed{ \underline{ \green{ \sf{ \therefore \: the \: area \: of \: triangle \: is \: 100 \sqrt{3} \: {cm}^{2} }}}}}$

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More about equilateral triangle:-

• An equilateral triangle is a triangle with all three sides of equal length.

• $\sf \: Area:  (\frac{ \sqrt{3} }{4} ) \: x \: ( side \: of \: equilateral \: triangle)²$

• Perimeter: 3 x side of equilateral triangle

• Number of vertices: 3

• Number of edges: 3

• Internal angle: 60°