Find the area of an equilateral
triangle having each side x cm.
Answers
Answer:
AREA OF THE EQUILATERAL TRIANGLE IS :
A= _/3/4×X²
Step-by-step explanation:
HOPE IT HELPS YOU...!
Let's try to figure out the formula.
W.k.t All the three sides of a equilateral triangle are equal.
Consider each side to be x cm.
∵ ABC is a equilateral triangle.
∴All the angles are 60 ° and AB=AC=BC= x cm
Let's construct a perpendicular on side BC (base side)
such that it passes through vertex A, and AD⊥BC
Now, ADB and ADC are two right angled triangles
And DB = DC = 1/2 BC = 1/2 x cm.
Using Pythagoras theorm in triangle ADB , D is a ⊾ triangle.
W.k.t (Hypotenuse)² = (Base)²+(Perpendicular)²
And (Perpendicular) = (Hypotenuse)²-(Base)²
Now applying it to the given triqngle ADB and ADC
AD =√(AB)²-(DB)²
AD = √(x)²-(x/2)²
Consider the identity
(a²-b²) = (a+b)(a-b)
AD = √(x+x/2)(x-x/2)
AD = √[{(2x+x)/2} {(2x-x)/2}]
AD = √ (3x/2) (x/2)
AD = √ (3x²/4)
AD = √(3) x/2
w.k.t AD is height of equilateral triangle ABC
Area of Equilateral triangle ABC=1/2×(base)×(height)
= 1/2×(x)×(√(3) x/2)
= √(3)x²/4
