This question was uploaded on 25/10/21 on social media accounts.
Find the ratio of the area between the equilateral triangle and the square to the complete area of the figure. Square is placed on the base of the triangle as shown in the figure.
Solution 1:
Now you can see 1 small equilateral triangle (1), one rectangle (3), and three 30-60-90 triangles (2, 4, 5).
Areas:
\[A_1=\frac{\sqrt3}4(\sqrt3-1)^2=\frac{\sqrt3}2(2-\sqrt3)\]
\[A_2=A_4=A_5=\frac{1\times\sqrt3}2=\frac{\sqrt3}2\]
\[A_3=\sqrt3(\sqrt3-1)\]
Blue fraction:
\[Fraction=\frac{A_3+A_4}{A_1+A_2+A_3+A_4+A_5}\]
\[\Rightarrow Fraction=\frac{2\sqrt3-1}{3+\sqrt3}=\frac{7\sqrt3-9}6\]
Puzzle related to Geometry, Square, Triangle, Ratio.
