Question

find the area of an equilateral triangle whose each side is 12 CM also find the height of triangle​

Answer 1

Answer:

Area of triangle=36√3 cm^2

and height=6√3 cm

Given:

An equilateral triangle whose each side is 12 cm

To find:-

Area of equilateral triangle and it's height

Solution:-

sides=12 cm

We know that

area of equilateral triangle

$= \frac{ \sqrt{3} }{4} {a}^{2}$

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

$= \frac{ \sqrt{3} }{4} \times 144$

$= \sqrt{3} \times 36$

$= 36 \sqrt{3} \: {cm}^{2}$

Now;

$area \: of \: triangle = \frac{1}{2} \times b \times h$

$= 36 \sqrt{3} = \frac{1}{2} \times 12 \times h$

$= 36 \sqrt{3} = 6h$

$h = \frac{36 \sqrt{3} }{6}$

$h = 6 \sqrt{3} \: cm$

----------------------------

$area \: of \: triangle = 36 \sqrt{3} \: {cm}^{2} and \: height = 6 \sqrt{3} \: cm$

Answer 2

$\huge{\underline{\underline{\mathrm{\red{GIVEN:-}}}}}$

• Side of an equilateral triangle is 12 cm

$\huge{\underline{\underline{\mathrm{\red{TO\:FIND:-}}}}}$

Find the Area of an equilateral triangle and the height of the triangle = ?

$\huge{\underline{\underline{\mathrm{\red{FORMULA \:USED:-}}}}}$

$\large{\boxed{\rm{\red{Area\:of\:Equilateral \:Triangle = \frac{\sqrt{3}}{4} \times {a}^{2}}}}}$

$\large{\boxed{\rm{\red{Area \:of\:Triangle = \frac{1}{2} \times b \times h}}}}$

$\huge{\underline{\underline{\mathrm{\red{SOLUTION:-}}}}}$

【We have given that, the sides of an equilateral triangle are 12 cm】

☞On putting the given values in the formula, we get

$\mathbf{Area = \frac{\sqrt{3}}{4} \times {(12)}^{2}}$

$\mathbf{Area = \frac{\sqrt{3}}{\cancel{4}} \times \cancel{144}}$

$\mathbf{Area = \sqrt{3} \times 36}$

➠$\large\mathbf\red{Area = 36\sqrt{3}\: {cm}^{2}}$

Thus, the area of an equilateral triangle is 36√3 cm²

⚫Now, we have to find the height of an equilateral triangle

☞On putting the given values in the formula, we get

$\large\mathbf{Area \:of\:Triangle = \frac{1}{2} \times b\times h}$

$\mathbf{36\sqrt{3} = \frac{1}{\cancel{2}} \times \cancel{12}\times h}$

$\mathbf{36\sqrt{3} = 6 h}$

$\mathbf{h = \large\frac{\cancel{36}\sqrt{3}}{ \cancel{6 }}}$

➠$\large\mathbf\red{h = 6\sqrt{3}\: cm}$

Thus, the height of an equilateral triangle is 6√3 cm