Answer: The area common to both triangle is 31.77 sq. cm.
Step-by-step explanation:
Since we have given that
30-60-90 triangles are placed.
So, the ratio of sides would be
[tex]1:\sqrt{3}:2[/tex]
Since Hypotenuse = 12 cm
So, it becomes,
[tex]2x=12\\\\x=\dfrac{12}{2}=6[/tex]
So, Base would be
[tex]x=6\ cm[/tex]
and Perpendicular would be
[tex]\sqrt{3}x=6\sqrt{3}[/tex]
So, Area common to the both triangles would be
[tex]\dfrac{1}{2}\times base\times height\\\\=\dfrac{1}{2}\times 6\times 6\sqrt{3}\\\\=18\sqrt{3}\\\\=31.177[/tex]
Hence, the area common to both triangle is 31.77 sq. cm.
