# Given a square with side #s# calculate the area of the curved square, (purple shade area in the figure to the left)? The 2nd figure is to the right is sketched to help guide your thinking?

Let the shaded area (U->T->U) be

Let area of

Let the area of the curved square in your diagram be

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To calculate the area of the curved square (purple shaded area in the figure), we first need to understand the construction. The figure shows a square with side length s and four quarter circles, each with radius s, added at the corners.

The area of the square is simply ( s^2 ). To find the area of the curved square, we need to subtract the areas of the quarter circles from the area of the square.

Since each quarter circle has a radius equal to the side length s of the square, the area of one quarter circle is ( \frac{1}{4} \pi s^2 ). Since there are four quarter circles, the total area of the quarter circles is ( 4 \cdot \frac{1}{4} \pi s^2 = \pi s^2 ).

Therefore, the area of the curved square (purple shaded area) is given by:

[ \text{Area of curved square} = \text{Area of square} - \text{Area of quarter circles} ] [ = s^2 - \pi s^2 ] [ = s^2(1 - \pi) ]

So, the area of the curved square is ( s^2(1 - \pi) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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