Q. 203.7( 3 Votes )

In an equilateral triangle with side a, prove that area = .

Answer :


Let ABC be the equilateral triangle whose side is a cm.


Let us draw altitude AD(h) such that AD BC.


We know that altitude bisects the opposite side.


So, BD = DC = a cm.


In ADC, ADC = 90°.


We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


So, by applying Pythagoras Theorem,


AC2 = AD2 + DC2


(a cm)2 = AD2 + (a/2 cm)2


a2 cm2 = AD2 + a2/4 cm2


AD2 = 3a2/4 cm2


AD = √3 a/2 cm = h


We know that area of a triangle = 1/2 × base × height


Ar(ΔABC) = 1/2 × a cm × √3 a/2 cm


ar(ΔABC) = √3 a2/4 cm2


Hence proved.


ar(ΔABC) = √3 a2/4 cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality TheoremBasic Proportionality TheoremBasic Proportionality Theorem42 mins
NCERT | Strong Your Basics of TrianglesNCERT | Strong Your Basics of TrianglesNCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs  From TrianglesRD Sharma | Imp. Qs  From TrianglesRD Sharma | Imp. Qs From Triangles41 mins
A Peep into Pythagoras TheoremA Peep into Pythagoras TheoremA Peep into Pythagoras Theorem43 mins
Predominant Proof of TrianglesPredominant Proof of TrianglesPredominant Proof of Triangles52 mins
R.D Sharma | Solve Exercise -4.2 and 4.3R.D Sharma | Solve Exercise -4.2 and 4.3R.D Sharma | Solve Exercise -4.2 and 4.345 mins
Quiz | Criterion of Similarity of TriangleQuiz | Criterion of Similarity of TriangleQuiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?How to Ace Maths in NTSE 2020?How to Ace Maths in NTSE 2020?36 mins
Champ Quiz | Thales TheoremChamp Quiz | Thales TheoremChamp Quiz | Thales Theorem49 mins
NCERT | Concept Based Questions on TrianglesNCERT | Concept Based Questions on TrianglesNCERT | Concept Based Questions on Triangles31 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses