Area of a figure

[Guest]

A square with side 4units is drawn. From all corners with radius 4 sectors with angle 90 degree are drawn. Now find the area of the common sector.

[Guest]

What is the question ??
You may post a diagram or else explain more clearly

[Guest]

Does nobody want this problem solved.?

I assume it is a square of length of each side is 4 units.

An Arc (quadrant) is drawn from each corner within the square. So 4 arcs overlapping each other.

This gives a curved cross X pattern with a "square shape" in the middle with curved sided.

I assume it is the area of this "curved square" that is required to be found.?

[Guest]

Just a simple solution....

You need to observe that there is a lot of symmetry in this construction.

If we join the curve intersection points we will form chords and segments of

the arcs and these will also form a square with straight sides. The area we

want to find will be the area of this square plus the area of the 4 segments.

The angle subtended by this chord to the corner of the large 4 unit square

will be 30 degrees.

The length of the chords will be = 2 x 4 x Sin 15 = 2.071 units
Area of the square part will be 2.071 x 2.071 = 4.287 sq units


Area of the segments = ((Pi x 4 x 4) / (12) = 4/3 x Pi) - Area of triangle

Area of triangle = 0.5 x 4 x 4 x Sin 15 = 4 sq units

So area of segment = ((4/3 x Pi) - 4) = 0.189

total for 4 of them = 0.757 sq units


So Area of curved Square 4.287 + 0.757 = 5.044 Sq Units.


.................Simple.............

[Guest]

Sorry.................

Above should read......

Area of triangle = 0.5 x 4 x 4 x Sin 30 = 4 sq units

............................................................

[AlanAnderson]

No, I am not getting your question clearly, can you draw a picture here?

[leesajohnson]

I would like to suggest you show us the image here so that we can understand the question easily.

[Guest]

What is the question ??
You may post a diagram or else explain more clearly

[Guest]

Hope this explains the bits that were not plain to see