Question

the altitude of an equilateral triangle is p cm. then area of this triangle

Answer 1

1/2 X p X base is the answer

Answer 2

ANSWER.


Equilateral triangle . The triangle whose all side

are equal and all three

interior angle are equal to

60°

ALL FORMULA OF EQUILATERAL ∆



$area \: = \frac{ \sqrt{3} }{4} \times {(side \:of \: equilateral \: triangle)}^{2}$


.
$area = \frac{ \sqrt{3} }{4} \times {(side)}^{2}$



$perimter \: = 3 \times side$


$hight = \frac{ \sqrt{3} }{2} \times side$




SOLUTION.


STEP 1.


Using hight formula ,



$hight = \frac{ \sqrt{3} }{2} \times side$

p is the altitude (hight) .......( GIVEN)


SO,


$p = \frac{ \sqrt{3} }{2} \times side$





$= > \frac{2p}{ \sqrt{3} } = side$




$= > side \: of \: a \: triangle = \frac{2p}{ \sqrt{3} }$



STEP 2.


Now using area formula,



$area = \frac{3}{4} {(side)}^{2}$


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



$= \frac{ \sqrt{3} }{4} \times \frac{4 {p}^{2} }{3}$




$= \frac{ \sqrt{3} \times {p}^{2} }{3}$



$\frac{ {p}^{2} }{ \sqrt{3} } {cm}^{2}$