Question

The height of the equilateral triangle is 6cm what will be it's area

Answer 1

height = 6cm

let the sides are a,b,c where a=b=c=x

x²=6²+(1/2x)²

x²-1/4x²=36

3x²/4=36

x²=36*4/3

x²=48

x=4√3

area = 1/2*2√3*6

area=6√3cm²

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Answer 2

$\textbf {Hey there, here is the solution.}$

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equilateral triangle = all sides have the same length

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STEP 1: Define x:

Let x be the length of side of the equilateral triangle

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STEP 2: Solve x:

Using Pythagoras' Theorem, a² + b² = c²:

a² + b² = c²:

(6)² + (x/2)² = x²

36 + x²/4 = x²

144 + x² = 4x²

3x² = 144

x² = 48

x = √48

x = 4√3 cm

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STEP 3: Find the area:

area = 1/2 x base x height

area = 1/2 x 4√3 x 6

area = 12√3 cm²

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Answer: The area of the equilateral triangle is 12√3 cm²

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⭐$\textbf {Cheers}$⭐