Question

If the height of an equilateral triangle is 15 cm, find its area.​

Answer 1

Answer:

Height=15cm

Let the side of the equilateral triangle be x

After drawing a figure we get:

${( \frac{x}{2} )}^{2} + {15}^{2} = {x}^{2}$

$\frac{ {x}^{2} }{4} + 225 = {x}^{2}$

${x}^{2} + 900 = 4 {x}^{2}$

$4 {x}^{2} - {x}^{2} = 900$

$3 {x}^{2} = 900$

${x}^{2} = 300$

x=√300

x=10√3

Now,

Since,

$Area \: \: of \: \: equilateral \: \: triangle= \frac{ \sqrt{3} {a}^{2} }{4}$

$= \frac{ \sqrt{3} }{4} \times 300$

=75√3

=75×1.732

=129.9cm^2

Answer 2

Answer:

Here is your answer....

Step-by-step explanation:

1. What is given?

Height of the equilateral triangle is 15 cm.

2.What is asked?

Area is asked.

We do not know the side, so let's keep it as 'a'

So to find the side,

√3/2 x a = 15

√3 x a = 15x2

√3 x a = 30

a = 30/√3

Now to find the area,

√3/4 x a²

we already found out the side(a) in previous steps

so,

√3/4 x 30/√3 x 30/√3

after reducing we will get

900/4√3

now we need to write this irrational form.

i. e 3 x 300/4√3

we can write 3 as √3 x √3

so,

√3 x √3 x 300/4√3

after reducing we will get

70√3

so the area = 70√3