Question

the area of an equilateral triangle whose side is " a " cm is √3/4 a^2 cm^2 . find its height​

Answer 1

GIVEN:

• Side of an equilateral triangle = a cm
• Area of an equilateral triangle = √3/4 a² cm²

TO FIND:

• What is the height of an equilateral triangle ?

SOLUTION:

We have given that, the side of an equilateral triangle is 'a' cm

We know that the formula for finding the height of an equilateral triangle is:-

$\bf{\star \: Height = \dfrac{\sqrt{3}}{2} \times a \: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow Height = \dfrac{\sqrt{3}}{2} \times a}$

$\bf{\dashrightarrow \star \: Height = \dfrac{\sqrt{3}}{2} a \: cm \: \star}$

❝ Hence, the height of an equilateral triangle is √3a/2 cm ❞

_____________________

✰ Extra Information ✰

➣ All sides of an equilateral triangle are equal in Length.

➣ The measure of each angle of an equilateral triangle is 60°

Answer 2

✬ Height = √3a/2 cm ✬

Step-by-step explanation:

Given:

• Side of equilateral triangle is a.
• Area of equilateral triangle is √3/4a² cm².

To Find:

• What is the height of equilateral triangle ?

Solution: Let ABC be a equilateral triangle where,

• AB = BC = CA = a cm
• AD = Height of ∆ = h cm
• BC = Base of ∆ = a cm

As we know that another formula for finding area of ∆ with base and height is

★ Area of Triangle = 1/2 (Base) (Height)★

According to the question:-

• Area of ∆ABC = √3/4a² or,
• 1/2 $\times$ Base $\times$ Height = √3/4a²

$\implies{\rm }$ 1/2 $\times$ BC $\times$ AD = √3/4a²

$\implies{\rm }$ 1/2 $\times$ a $\times$ h = √3/4 $\times$ a $\times$ a

$\implies{\rm }$ h/2 = √3a/4

$\implies{\rm }$ h = √3a/4 $\times$ 2

$\implies{\rm }$ h = √3a/2

Hence, the height of equilateral triangle is AD = h = √3a/2 cm