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# Help getting an equation for the area of this shape watch

1. So the shape is like a rectangular base with a semi-circle on top of that rectangle. In such a way that the base of the rectangle is 2r. The perimeter is 40cm.

Show that A=40r - 2r^2 - (pi*r^2)/2.

I began by calling h the height of the rectangle part and setting:

2rh+pi*r = 40.
Then I thought maybe I could do an equation for the area of the triangle, make h the subject of that equation and substitute that into the equation stated above. So I tried but can't really do it.

Any suggestions?
2. (Original post by olly_price)
So the shape is like a rectangular base with a semi-circle on top of that rectangle. In such a way that the base of the rectangle is 2r. The perimeter is 40cm.

Show that A=40r - 2r^2 - (pi*r^2)/2.

I began by calling h the height of the rectangle part and setting:

2rd+pi*r = 40.
Then I thought maybe I could do an equation for the area of the triangle, make h the subject of that equation and substitute that into the equation stated above. So I tried but can't really do it.

Any suggestions?
How did you get 2rd+pi*r=40?
Surely it should have been 2r+2h+pi*r=40
A=2rh+(pi*r^2)/2 and substituting for h will give the required result.

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Updated: May 20, 2013
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