Question

The side of an equilateral triangle is 14 cm. Find its area (in sq.cm).

A) 64√3 B) 49√2 C) 64√2 D) 49√3

Answer 1

Given :

• The side of an equilateral triangle = 14 cm.

To find :

• The area of equilateral traingle =?

Formula Used :

• Area of equilateral traingle = (√3/4)a²

Step-by-step explanation :

As We know that,

Area of equilateral traingle = (√3/4)a²

Substituting the values in the above formula, we get,

= (√3/4)(14)²

= (√3/4)14 × 14

= (√3/4) × 196

= √3 × 49

= 49√3

Therefore, Area of equilateral traingle = 49√3 cm².

Hence,

Option d). 49√3 cm² is the correct option.

Answer 2

Answer:

⋆ DIAGRAM :

⠀⠀⠀$\setlength{\unitlength}{1.8cm}\begin{picture}\thicklines\put(8,1){\line(1,0){3}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8.1,1.8){\sf{14 cm}}\put(10.3,1.8){\sf{14 cm}}\put(9.3,0.75){\sf{14 cm}}\end{picture}$

⠀⠀⠀$\rule{160}{1}$

☢ $\underline{\textsf{According to the Question now :}}$

$\dashrightarrow\sf\:\:Area\:of\: Equilateral\:\Delta=\dfrac{\sqrt{3}}{4} \times (Side)^2\\\\\\\dashrightarrow\sf\:\:Area\:of\: Equilateral\:\Delta=\dfrac{\sqrt{3}}{4} \times (14\:cm)^2\\\\\\\dashrightarrow\sf\:\:Area\:of\: Equilateral\:\Delta=\dfrac{\sqrt{3}}{4} \times 196\:cm^2 \\\\\\\dashrightarrow\sf\:\:Area\:of\: Equilateral\:\Delta=\sqrt{3}\times 49\:cm^2\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: Equilateral\:\Delta=49\sqrt{3}\:cm^2}}$

⠀

$\therefore\:\underline{\textsf{Hence, Area of equilateral \Delta is B) \textbf{49 \sqrt{\text3} cm ^\text2 }}}.$