Question

Show that area of an equilateral triangle is √3/4×a^2, where a is the measure of each side of the equilateral triangle.

Answer 1

Answer: Area of a equilateral triangle

= √3/4 ×a^2

Where a is the side of the equilateral triangle.

Now let's prove that using some trigonometry.

As you can see in the above image all the angles in an equilateral triangle are 60° and all the sides are congruent, which is represented as a.

Now, area of triangle= 1/2 ×base × height

Let's find out the base and height.

Base= BC = a

Angle ABD= 60°

Sin B = opposite side/hypotenuse

Sin60= AD/AB

√3/2= height/a [ since, sin60= √3/2]

Height= √3/2× a

Now we have both height and base,so let's substitute it in the formula.

Area of equilateral triangle= 1/2× base× height

= 1/2× a× √3/2× a

= √3/4 ×a^2

So, it is proved

Answer 2

Answer:

Step-by-step explanation: