Question

The height of an equilateral triangle is √3a units. Then its area is equal
to ______________.
Answer will be a²√3.​

Answer 1

Step-by-step explanation:

Area of equilteral triangle=(√3)(side)²/4

Here Let one side=x

So, H²= B²+P²

x²= x²/4+ (√3a) ²

x²-x²/4= 3a²

3x²/4 =3a²

x²= 4a²

Area= (√3× 4a² ) /4

= a²√3

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Answer 2

GiVen :-

• triangle is equilateral
• height of triangle= √3a

To find :-

• area of triangle

Solution :-

$\red{ \mathtt{height \: of \: a \: equilateral \: triangle \: = \frac{ \sqrt{3} }{2} side}} \\ \\ { \mathfrak{putting \: the \: value \: of \: height}} \\ \\ { \mathtt{\frac{ \sqrt{3} }{2} side = \sqrt{3}a }} \\ \\ { \mathfrak{hence \: side \: is \: 2a}} \\ \\ { \mathtt{using \: herons \: formula}} = \sqrt{s(s - a)( s- b)(s - c)} \: \: \: \: \: \: \: where \: s \: is \: semi - perimeter \\ \\ \pink{ \mathtt{s = \: \frac{2a + 2a + 2a}{2} = 3a}} \\ \\ { \mathfrak{putting \: values \: of \: a \: \: b \: \: c \: and \: s}} \\ \implies \sqrt{3a(3a - 2a)(3a - 2a)(3a - 2a)} \\ \\ \implies \sqrt{3a \times a \times a \times a} \\ \\ \implies \sqrt{3 \times {a}^{4} } \\ \\ \implies {a}^{2} \sqrt{3}$

$\huge{\bf\orange{Hence, \: the\: area\: of\: triangle\: is \:{a}^{2}\sqrt{3}}}$