Since all the circles have the same radius Therefore they have equal areas Area of a circle equals pi (r) squared = 10^2×pi = 100pi cm^2 Lets join the centres of the circles and make a square of side 10+10 = 20 cm The area of this square= 20 × 20= 400cm^2 The area of the included part between the circles, equals the area of the square - the area of one circle ( quarter of circle + quarter of a circle + quarter of a circle +quarter of a circle

since they are "equal in radius")

400 - 100pi cm^2 Adding area of all shaded parts: Included part = 400-100pi Area of the circle = 100pi So area = 400 -100pi +100pi Wich is equal 400 cm^2 :)

Join the adjacent centers of the circle, it will make up a square of $(20 \times 20 ) cm^{2}$

now subtract the area of quadrant of 4 circles to get the area of the blue portion in the middle that is $(4 \times \frac{1}{4} \times pi \times r^{2}) cm^{2}$ and then add the area of the blue circle, which is $(pi \times r^{2} ) cm^{2}$

Thus the formula comes out to be. $(20 \times 20)cm^{2} - (4 \times \frac{1}{4} \times pi \times r^{2})cm^{2} + (pi \times r^{2})cm^{2}$

Its so simple. divide the four side star vertically and horizontally right at the mid, then move it around the blue circle until it make a perfect square.

The four parts "lost" when taking the circle out of the 20 x 20cm square in which it was inscribed you can use them to build the blue figure in the middle of the four circles. Therefore the blue area is 20 x 20.

the blue shaded origin is actually a square if we rearrange . the area is equal to square of(10*2) = 400

tricky. all four circle's part pi r^2 and total pi r^2 of a single circle crosses each other.

The middle blue section can be divided into four equal pieces, which can be placed around the bottom-right circle. From there you can see that the blue section is equal to the square of the circle's diameter, and solve accordingly (sorry, no visual).

You can break the star-shaped blue part into 4, and put them around the blue circle, like so:

The blue square now obviously has the same area as the original blue-shaded area, which is the area that was asked for. So that's a square of 20 x 20, with an area of $\boxed{400}$

Or simply encase the blue circle in a square, then realise the rest of blue area completes the square and then just calculate the area of that square. Radius of a circle would be half of the side, so 2x10=20 (side) and then 20 squared is 400.

Make a square whose vertices are the centres of four circles. Side of square will be 20 cm. Area=400 cm sq. If we look at one of the 4 circles, the part of the square divides it into 1/4. There are 4 such parts( these parts look like half semi-circle or 1/4 th of a complete circle). We will find the area of one such part by pie r sq/4. As there are 4 such parts so the total area of them are pie r sq. Area of the region formed between these circles=Area of square-area of the four parts. 400-2200/7=600/7 cm sq. Area of the blue region=600/7+Area of the blue circle=600+2200/7=2800/7=400 cm sq

Area of square enclosing the middle section = (10 cm + 10 cm)^2 = 400 cm^2 Area of 4 quarter sectors = Area of entire circle with radius 10 cm = 100pi cm^2 Area of shaded area = 400 - 100pi + 100pi = 400 cm^2

The blue shaded circle can be divided into four quadrants and "distributed" equally to all circles. By proper arrangement, it will form a shaded blue square with one side equal to the diameter of the circle. Therefore, the area of the shaded blue part is 400 cm^2.

Draw the square whose vertices are the centers of the four circles . obviously the length of each edge of the this square is 20 cm and the its area is equal to 20×20=400 cm². now our mission is to calculate the area of the middle blue section . Note that the area of the square drawn is equal to the area of the blue shape besides the area of the quarters of circles , in other words , the area of the blue shape equals 400 cm² - 100 pi cm².. knowing the area of the blue circle gets the total required area which is equal to 400-100 pi +100 pi = 400 cm² .

Just redistribute the area from circle over the square... and we can see a square from side 20! So 20 x 20 = 400.

a square formed by joining the centers (minus) the area of 4 sectors,i.e, the area of the circle gives u the middle part: 20^2 - (pi x 10^2)= 400 - pi 100 sq cm. now add the area of one whole blue circle . 400 - pi 100 + pi 100= 400 sq cm!!!

(10 + 10)^2 = 400

20x20= 200

10+10=20. 20 squar = 400 = 1/3 of 4 circles. which is equal of 1 circle and other blue area .