A,B,C and D are points on a circle. ABCD is a square of side 7 cm. Work out the total area of the shaded regions. Give your answer correct to the nearest whole number.
To work out the shaded area, we first need to calculate the area of the square and the area of the circle. The shaded area is equal to the area of the circle minus the area of the square.
The area of the square is length times width, which would be 7 * 7 = 49 cm squared.
The area of the circle is π * r * r . We do not have the radius of the circle, but we can calculated the diameter using pythagoras' theorem (a^2 + b^2 = c^2). c^2 = 7^2 + 7^2 = 49 +49 = 98. Since c squared = 98, c ( the diameter of the circle) is the square root of 98 or 7 root 2. From this we can calculate the radius as (7 root 2)/2. We can put our value for the radius into the equation π * r * r to get the area of the circle which is 76.97(2 d.p)
Therefore the area of the shaded region is equal to 76.97 - 49, which equals 27.96. So the answer will be 28 as we need to round to the nearest whole number.
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