Question

If the altitude of an equilateral triangle is 12 √3 cm, then its area would be :

Answer 1

check your answer on the image I have attached.

Answer 2

Answer :

The area of the equilateral triangle is 144 √ 3 cm²

Step-by-step explanation :

We know that ;

Altitude of an equilateral triangle =
√3 / 2 * a.

We have ;

$\sf \frac{ \sqrt{3}a }{2} = 12 \sqrt{3} \\ \\ \sf \sqrt{3a} = 24 \sqrt{3} \\ \\ \sf \therefore a = 24$

Area of triangle =

$\sf \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \sf \frac{ \sqrt{3} }{4} \times 24 \times 24 \\ \\ \sf \sqrt{3} \times 6 \times 24 \\ \\ \sf 144 \sqrt{3}$

Hence, the area of the equilateral triangle is 144√3 cm²