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  • Each side of an equilateral triangle measures a unit. Then the area of the triangle is <img alt="\frac{\sqrt3}{4}a^2\;" src="https://learn.careers360.com/latex-image/?%5Cfrac%7B%5Csqrt3%7

Each side of an equilateral triangle measures a unit. Then the area of the triangle is \frac{\sqrt3}{4}a^2\; sq. unit.

Option: 1

True


Option: 2

False


Answers (1)

best_answer

Let an equilateral triangle ABC with each side a unit.

Take the mid-point of BC as D and join it to A. We know that ADB is a right triangle. 

Therefore, by using Pythagoras Theorem, we can find the length AD as shown below:

              AB2 = AD2 + BD2

i.e.        (a)2 = AD2 +  (a/2)2 , since, BD = DC

Therefore, we have AD2  = (a)2 -  (a/2)2 = (3a2/4)

\text{AD} = \frac{\sqrt3}{2}a\;\text{unit}

Then area of ? ABC = \frac{1}{2} \times \text { base } \times \text { height }=\frac{1}{2} \times(a)\times \left ( \frac{\sqrt3}{2}a \right )= \frac{\sqrt3}{4}a^2 \text{sq. unit}

 

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