Question

the side of an equilateral triangle is 12 cm and its semi perimeter is 18 cm. what is the area?​

Answer 1

Ok so formula of equilateral triangle is = √3/4 × 18 × 18

√3/4 × 324

√3 × 81

1.732 × 81

= 140.292 cm^2

Answer 2

$\bf \underline {\underbrace{Understanding \: the \: Concept }}$

Before solving this question, you must the Herons Formula and special formula of finding equilateral triangle (that is also derived by Heron's Formula. This Formula you would study in Class 9. If you know the formula, fol.low me up and let's cr. ack this question.

$\bf Given :$

$\sf{ \implies side \: of \: equilateral \triangle = 12cm}$

$\sf{ \implies perimeter \: of \: the \triangle = 18cm}$

$\bf{ \underline{ \underbrace{Formula \: to \: be \: Used }}}$

$\longmapsto \sf{Heron's \: Formula : }$

$\sf{\sqrt{s(s - a)( s- b)( s- c)} }$

Where s is the semi- perimeter of the triangle and a,b,c are the sides of the triangle. and the formula of semi perimeter can be stated as $\sf{\frac{a+b+c}{2}}$

$\longmapsto \sf{Area \: of \: Equilateral \triangle : }$

$\sf{\frac{\sqrt{3}}{4} \times (side)^2}$

$\bf{ \underline{ \underbrace{Solution }}}$

$\sf{ \implies \frac{\sqrt{3}}{4} \times (12)^2}$

$\sf{\implies\frac{\sqrt{3}}{\cancel4} \times \cancel{12} × 12}$

$\sf{ \implies \sqrt{3} ×3×12}$

$\sf\pink\Large{\implies 36\sqrt{3}}$