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It's a rectangle with 2 half elipses joined on the left and right side.

The rectangle itself is 3.55 X 2.54

The width of the whole shape (rectangle with 2 elipses) is 4.195.

Take away the width of the rectangle from the overall width

4.195 - 2.54 = 1.656

1.655 is the width of the 2 elipses. (0.8725 each)

Because I have the width of the 2 elipses as 1.655 when put together and the height as 3.55 can I accurately calculate the the area of the full shape?

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A drawing would help! – Nicky Hekster Jun 20 '14 at 7:58

The ellipses are the real problem here, the square shouldn't be very hard to tackle.

We have 2 identical half ellipses, giving us one full ellipse. Here's the dimensions if the ellipse:

$1.655 \text{ by }3.55$

The area of the ellipse is then $\pi\times 0.8275\times1.75$

Adding the area of the square gives us $$\pi\times 1.75\times0.8275+3.55\times2.54=1.448125\pi+9.017\approx13.566$$

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For calculating the elipse do you not use the length of the semi major and minus axis? Ie pi X half height X half width? So it would be pi X 1.75 X 0.8275 – user158164 Jun 20 '14 at 9:24
@user158164 you're right, I'll edit my answer – Kristoffer Ryhl Jun 20 '14 at 9:31
I did the exact same as you but I'm not sure how accurate it is. Posted it on and got a different answer. – user158164 Jun 20 '14 at 10:10 this is the original question – user158164 Jun 20 '14 at 10:11
@user158164 On your answer you set $R=2.098$ where it actually is $R=2.183$ this has the effect of having the angle off by $6.7$ degrees, and such propagates with the error increasing for each step. Finally this causes the error in your final answer. – Kristoffer Ryhl Jun 20 '14 at 10:39

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