Question

Find the area of an equilateral triangle having side of 20m length.also find its attitude

Answer 1

Hi friend, Harish here:

Here is your answer:

Given that,

1) It is an equilateral triangle.

2) Side of the triangle is 20 cm.

To find,

The area of the equilateral triangle. And Altitude. 

Solution,

We know that,

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

Here a is the side of the triangle.

Then,

$Area = \frac{ \sqrt{3} \times 20^{2} }{4}$

→  $\frac{ \sqrt{3}\times 400 }{4}$

→  $100\sqrt{3}\ cm^{2}$

Therefore area of the equilateral triangle is 100√3 cm².

ii)  Refer to the image for the Markings.

Here , BD is the altitude of the equilateral triangle.

We know that,

Angle BD = 90°.  And AD is half of AC  = 10 cm.

So, Use Pythagoras Theorem .

Then, 

$BD = \sqrt{AB^{2}- AD^{2}}$

→ $= \sqrt{20^{2} - 10^{2}}$

→ $\sqrt{400 - 100}$

→ $\sqrt{300}$

→ $10 \sqrt{3} \ cm$

Therefore altitude of the triangle is 10√3 cm.
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Hope my answer is helpful to you.