SOLUTION: A circular pond will be placed on a square piece of land.The length of a side of the square is 2x.The radius of the pond is x.The part of the square not covered by the pond will be

Question 128341: A circular pond will be placed on a square piece of land.The length of a side of the square is 2x.The radius of the pond is x.The part of the square not covered by the pond will be planted with flowers.What's the area of the region that will be planted with flowers?Write your answer in factored form.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Although it is not necessary to do so in solving this problem, try to envision a picture of
what the pond and the square area look like. The circular pond has a diameter of twice its
radius, and since the radius is x, the diameter of the circle is 2x. But the length of the
side of the square is also 2x. Therefore, the circle is inscribed in the square such that
the circle will touch all four sides of the square. The center of the circle will be exactly
at the point where the two diagonals of the square cross.
.
What you are trying to find is the total area of the four regions that lie outside the circle
but inside the square.
.
To do that, just find the area of the square and from that area subtract the area of the
circle. The difference will be the total area of the four odd-shaped pieces.
.
The area of the square is found by multiplying two of its sides. This area is:
.

.
And the area of the circular pond is found by squaring its radius and multiplying that
result by pi. For this problem that area is:
.

.
The total area of the four odd shaped pieces is the area of the garden and is equal to
the differences of the two areas we found above. The garden area is:
.

.
And if you prefer, you can factor the to write the garden area as:
.

.
Hope this helps you to understand the problem and how to solve it.
.

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