Answer: 16.205 cm²
It takes some time, but it's not impossible!
Explanation:
Find the area of the triangle, then subtract the area of the three sectors.
The three sectors are each 60° so they add to 180° which is equivalent to half the area of one circle.
The area of the triangle is one half base times height. To find the height of the triangle, use the Pythagorean Theorem to get the length of the perpendicular bisector.
a² + b² = c² .
C is the side length, 20cm. (the length of two radii) B is half the side length 10cm. A is the "altitude" or height we need to find.
a² + 10² = 20²
a² + 100 = 400 . a² = 400-100
a² = 300
a = √300 a ≈ 17.3205
Area of triangle: A= bh/2
A = (20 × 173.205)/2
Triangle Total Area ≈ 173.205
To the area of the circle, use the equation A = πr²
A = 3.14 × 10²
A = 3.14 × 100
Circle Total Area = 314 cm².
You could take 1/6 of that, and then multiply by 3, or just take half
Area of sectors= 157 cm²
Triangle Area - Sectors Area = Blue shape Area
173.205 - 157 ≈ 16.205 cm²