Triangle,Fractions,Maths

What fraction is the shaded area of the equilateral triangle?

Triangle,Fractions,Maths

What fraction is the shaded area of the equilateral triangle?

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SAngaku-3  http://mathematicsbhilai.blogspot.in/2012/04/sangaku-3.html

SAngaku-3 http://mathematicsbhilai.blogspot.in/2012/04/sangaku-3.html

Problem from the sangaku of the Eiryuji Temple.  In the right triangle ABC , a circular arc is drawn with the center A . A square lies between the arc and the triangle. If the side of the square is maximal, find the height AC and the side of  the square in terms of base BC .

Problem from the sangaku of the Eiryuji Temple. In the right triangle ABC , a circular arc is drawn with the center A . A square lies between the arc and the triangle. If the side of the square is maximal, find the height AC and the side of the square in terms of base BC .

Problem from Ten'nenji Temple. ABC is a regular triangle, and three congruent squares touch ABC triangle internally. And the three congruent squares touch at J, K and L , as shown. If the side of the triangle is a, the side of the square is x , find x in terms of a .

Problem from Ten'nenji Temple. ABC is a regular triangle, and three congruent squares touch ABC triangle internally. And the three congruent squares touch at J, K and L , as shown. If the side of the triangle is a, the side of the square is x , find x in terms of a .

What fraction is shaded?

What fraction is shaded?

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