Prove that the area of an equilateral triangle is equal to √3÷4×a² where a is the side of the triangle.
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base of equilateral triangle = b
height = square root of(side² - (side/2)² by pythagoras theorem
= √s²-s²÷4
= √(4s²-s²)/4
=√3s²/4
= √3 x s/2
area = 1/2 x b x h
= 1/2 x s x √3 x s/²
= √3/4 s²
height = square root of(side² - (side/2)² by pythagoras theorem
= √s²-s²÷4
= √(4s²-s²)/4
=√3s²/4
= √3 x s/2
area = 1/2 x b x h
= 1/2 x s x √3 x s/²
= √3/4 s²
hardyk09:
no prob guga
Answered by
11
A line perpendicular to the the opposite base which will form 2 right angle triangles. Each right triangle leg length x/2.
according to the pythagorean theorem :
Each right angle triangle area is . And the area of the equilateral triangle is double of that.
( a can be x) ( means √)
according to the pythagorean theorem :
Each right angle triangle area is . And the area of the equilateral triangle is double of that.
( a can be x) ( means √)
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