Question

Derive the formula to find area of equilateral triangle.. Please explain every step. I will mark brainliest

Answer 1

root 3/4 a square is the answer

Answer 2

SOLUTION:-

➡️Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”.By drawing perpendicular from A, we get two congurent right triangle ABD and ADC.

➡️Area of triangle ABC  =  Area of triangle ABD + Area of triangle ADC

➡️Since triangles ABD and ADC are congurent, areas will be equal.

Area of triangle ABC  =  Area of ABD + Area of ADC

Area of triangle ABC  =  2  (Area of ABD)

=  2 × (1/2) ⋅ Base ⋅ Height

Area of triangle ABC  =  Base × Height  ---(1)

In triangle ABD,

Base (BD)  =  a/2 and height (AD)  =  h

➡️Using Pythagorean theorem,

a²  =  h² + (a/2)²

h²  =  a² - (a²/4)

h²  =  (3a²/4)

h  =  √(3a²/4)

h  =  (a√3/2)

➡️By applying the values of base and height in (1), we get

➡️Area of triangle ABC  =  (a/2) ⋅ (a√3/2)

 

=  (1/4)a²√3

Area of triangle ABC  =  √3a²/4 square units