Question

The height of an equilateral triangle is 6cm, then the area of the triangle is

a) 15
3‾√
cm2 b) 3
3‾√
cm2 c) 12
3‾√
cm2 d) 4
3‾√
cm2

Answer 1

Given,

The height of the given equilateral triangle = 6 cm

To find,

The area of the given equilateral triangle.

Solution,

Let, the length of each sides of the given equilateral triangle = a cm

Height of the given equilateral triangle

= ✓3/2 a cm

According to the data mentioned in the question,

✓3/2 a = 6

a = 6 × 2/✓3

a = 12/✓3

a = 3×4/✓3

a = 4✓3

Length of each sides of the given triangle = 4✓3 cm

So. the area of the given equilateral triangle,

Area = ✓3/4 (a)² = ✓3/4 × (4✓3)² = ✓3/4 × 48 = 12✓3 cm²

Hence, the area of the given equilateral triangle is 12✓3 cm².

Answer 2

$Given \: height \: of \:an \: equilateral \\triangle (h) = 6 \:cm$

$Let \: side \: of \: the \: triangle = a \:cm$

/* We know that */

$\frac{\sqrt{3}}{2} a = h$

$\implies a = \frac{2}{\sqrt{3}} h$

$\implies a = \frac{2}{\sqrt{3}} \times 6$

$\implies a = \frac{12}{\sqrt{3}} \: --(1)$

$\red{ Area \: of \: the \: triangle } \\= \frac{\sqrt{3}}{4} a^{2}\\= \frac{\sqrt{3}}{4} \times \Big( \frac{12}{\sqrt{3}}\Big)^{2} \\= \frac{\sqrt{3}}{4} \times \frac{144}{3} \\= 12\sqrt{3} \:cm^{2}$

Therefore.,

$Option \: \green { ( c ) } \:is \: correct$

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