Can anyone calculate the area of the top shape in this diagram?

Question

http://postimg.org/image/w5f5moq7z/

The top shape on the diagram is the sensor that I need to calculate the area for. I have tried using the 2 elipses at the side and combining them together to get a full elipse but I'm not sure how accurate that is

Answer 1

Hint: You have a circle with radius $2.0975$ with part of the circle removed top and bottom(radius here 1.775).

$4\int_0^{1.775} \int_0^{\sqrt{(2.0975)^2 - y^2}} 1 \;\mathrm{d}x \; \mathrm{d}y$, Or you can you alternative coordinates. Note: I haven't used $\pm$ here, but I am sure you can work out the method(assuming some calculus has been obtained).

Note: The above text tells us that it was a circle with top and bottom removed. Hence the basis of my method.

Above evaluates to $4*3.21114 = 12.8446$(unit)$^2$, and this is your answer.

Below we have the entire region plotted, and under it the integral of the region in totality, below that we have my first method(I broke the region into four parts and integrated it, and multiplied by four), with it's integral underneath it. Note these integrals evaluate to be one and the same.

Answer 2

The centre square is, assuming Max area, 2.54mm by 3.55mm giving an area of: 9.017mm

Each segment has a base (h) of 3.55mm and a height (c):of 1.01mm.

Using this information we can calculate the radius (R) of the circle that the sectors would be a part of: R=h/2 + c²/8h R=1.902

The angle (a, rad) that forms the sector is given by: a = 2arcsin(c/2R)

Giving the nice result that is almost pi radians.

Area is found by then using the information gathered thus:

A = (R²/2)(a - sin(a)) = 5.67mm (Max area)