SOLUTION: ABCD is a square and semicircles are constructed on each side of the square. if AB is 2, what is the area of the entire ?

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Question 478955: ABCD is a square and semicircles are constructed on each side of the square. if AB is 2, what is the area of the entire ?
Answer by Jstrasner(112) About Me  (Show Source):
You can put this solution on YOUR website!
Hey,
So for this one we need to find the area of the square and the 4 semicircles around it. The area of a square is the length times the width. Therefore:
2 x 2 = 4
Now we need to find the area of the 4 semicircles. The area of a whole circle is
π (pi) x radius^2
If the diameter of the circle is 2 then the radius is 1. Therefore the area of on of the semicircles is: 1/2 x π x 1^2 = (1/2)π and since there are 4 semicircles you multiply that by 4: (1/2)π x 4 = 2π
Now you simply need to add the area of the square and the semicircles:
4 + 2π = 4 + 2π
Since π is a different variable than a number, the two units cannot be added into on unit. However, you can leave the answer as: 4 + 2π
I hope this helps!