Question

A circle of radius 6 cm is divided into 6 equal sectors an equilateral triangle is drawn on the chord of each sector to lie outside the circle

Answer 1

The area of resulting figure is 183.52 sq miter.
Step-by-step explanation:
We can understand that all the angle subtended at the center of circle have equal measures. Because all the triangles (MGH, MHL, MKL, MKJ, MJI, MIG) are made by radii of the circle and all the sectors are equal. So all the triangles are isosceles triangle.
Here, we consider first. (Refer the figure attached)
We draw a perpendicular MN from M to JK.
From
Let, MN = h
JK is the chord of circle.

So,
We know that,
length of chord
=
JK = 6 cm
NK = 3 cm
Now,


h = 5 cm,  Because h is the length.
Now, the area of
=
= 15 sq miter (All the triangles as MJK, MKL, MLH, MHG, MGI, MIJ ) have same area.
Now, the triangle out side \Delta JKD is an equilateral triangle. Its side length is equal to chord of the circle.
So, the area of


All the outside triangles have the same area as sq miter.
Thus, the resulting figure area = All inner triangle's area + All outer triangle's area

= 90 + 93.52
= 183.52 sq miter
Thus, the area of resulting figure is 183.52 sq miter.

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