ABCD is a square of side 10 cm. Each side of the square is a tangent to the circle. Work out the total area of the shaded regions in terms of . Give your answer in its simplest form.
Here it's best to start this question off by drawing a diagram.
Draw a square with each side having a length of 10cm and a circle which touches each side of the square only once (as eacn side of the square is a tangent to the circle).
Once drawn we can see that the area we need to find out is the area of the square - the area of the circle.
It is easy to find the area of the square since this is just the length x width; in this case this is 10cm x 10cm so the sqaure's area is 100cm2.
The formula to find the area of a circle is π x r2.
We know the diameter of the circle is 10cm as one edge of the circle to the other edge is equal in length as one edge of the square (as seen from the diagram). The radius is equal to 1/2 * diameter therefore the radius here is 5cm and the area of the circle is 5cm * 5cm * π = 25π cm2 .
Therefore the shaded are = 100-25π cm2.
