Find the Area of the Four Petals Inside a Square

In this video we find the area of the four green petals inside the square in which each side is equal to 6 inches.

[اممدنحمظ]

تمرين جميل جيد . رسم واضح مرتب . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين

[patrickakunna]

An alternate solution is to find the area of half a petal and multiply it by 8. ie determine 8x (Area of quadrant -inscribed triangle) = 8(9pi/4 -9/3) =20.52

[TheEulerID]

I did it by a different technique. Construct a right angle isosceles triangle from the middle of the square's base, to the centre of the square and then with the hypotenuse down to the lower right corner. The hypotenuse makes a chord of the lower half circle, and the segment is half the area of a petal. The area of the segment is simply the area of a quarter circle of radius 3 less that of the 3 x 3 right angle triangle.

The segment area Pi * 3 * 3 / 4 - 3 x 3 / 2. Multiply that by 8 (for the 8 half-petals) and we get 18 * Pi - 36.