Hi
dave13, How have you been?
No - there is no such formula ( at least not that I know of, or within the scope of GMAT)
So, this question is testing three things -
1. Area of an equilateral triangle. (
Also the fact that all angles are equal to 60 degrees in one)2. 30-60-90 triangle side ratios
3. Area of a right-angled triangle.
My thought process -
Okay. We need to find the area of an unual looking quadrilateral. Let's try to find the area of the two regular triangles that we know of and subtract the smaller one from the larger triangle to find the unusual area.
The side of the equilateral triangle is 3 so its area is \(\frac{s^2}{4}*\sqrt{3}\)
remember this - comes handy \(\frac{3^2}{4}*\sqrt{3}\)
\(\frac{9}{4}*\sqrt{3}\)The smaller triangle is 30-60-90 (one angle is 90 degrees and one angle is common between itself and the equilateral triangle)
Okay, so the side ratios of a 30-60-90 triangle are 1, \(\sqrt{3}\) and 2 with the smallest side being opposite the smallest angle.
This implies area of right angle triangle is -
\(\frac{1}{2}b*h\)
\(\frac{1}{2}*\sqrt{3}\)So the area we are interested in will be the difference -
\(\frac{9}{4}*\sqrt{3} - \frac{1}{2}*\sqrt{3}\)
\(\frac{7}{4}*\sqrt{3}\)
Hope this helps. Have a nice day.
dave13 wrote:
what is the formula of area of an irregular quadrilateral ?
_________________
Regards,
Gladi
“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)