Question

If the altitude of an equilateral triangle is √12 cm, then its area is equal to :

Answer 1

12= x2+x2

x2=6x =root of 6

area =root 12 ×root6×1/2

root of 72 ×1/2

2 root 18 ×1/2

root 18

3root2

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Answer 2

The area of the equilateral triangle is 144 √

The area of the equilateral triangle is 144 √ We know that ;

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.We have ;

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.We have ;\begin{gathered}\sf \frac{ \sqrt{3}a }{2} = 12 \sqrt{3} \\ \\ \sf \sqrt{3a} = 24 \sqrt{3} \\ \\ \sf \therefore a = 24\end{gathered}23a=1233a=243∴a=24

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.We have ;\begin{gathered}\sf \frac{ \sqrt{3}a }{2} = 12 \sqrt{3} \\ \\ \sf \sqrt{3a} = 24 \sqrt{3} \\ \\ \sf \therefore a = 24\end{gathered}23a=1233a=243∴a=24Area of triangle =

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.We have ;\begin{gathered}\sf \frac{ \sqrt{3}a }{2} = 12 \sqrt{3} \\ \\ \sf \sqrt{3a} = 24 \sqrt{3} \\ \\ \sf \therefore a = 24\end{gathered}23a=1233a=243∴a=24Area of triangle =\begin{gathered}\sf \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \sf \frac{ \sqrt{3} }{4} \times 24 \times 24 \\ \\ \sf \sqrt{3} \times 6 \times 24 \\ \\ \sf 144 \sqrt{3}\end{gathered}43a243×24×243×6×241443

The area of the equilateral triangle is 144 √ We know that ;Altitude of an equilateral triangle =√3 / 2 * a.We have ;\begin{gathered}\sf \frac{ \sqrt{3}a }{2} = 12 \sqrt{3} \\ \\ \sf \sqrt{3a} = 24 \sqrt{3} \\ \\ \sf \therefore a = 24\end{gathered}23a=1233a=243∴a=24Area of triangle =\begin{gathered}\sf \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \sf \frac{ \sqrt{3} }{4} \times 24 \times 24 \\ \\ \sf \sqrt{3} \times 6 \times 24 \\ \\ \sf 144 \sqrt{3}\end{gathered}43a243×24×243×6×241443Hence, the area of the equilateral triangle is 144√3 cm².

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