MediumMathematicsHigh School (9–10)Mensuration › Areas and PerimetersNumericalBoard Exam SAT

figure: ar-a3-quarters.png A square has a side of 35 cm…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A square ABCD with side a, with A at the bottom left and C at the top right. At each corner, a quarter of a circle of radius a over 2 is drawn with its centre at the corner, so that neighbouring quarter circles touch at the middle of each side. The middle region that is not inside any quarter circle is shaded orange and labelled shaded. One radius at A is drawn in green.

A square has a side of $35\ \text{cm}$ . A quarter circle of radius $17.5\ \text{cm}$ is drawn at each corner, with its centre at the corner. Find the area of the middle region that is not covered. Take $\pi = \dfrac{22}{7}$ .

Need a reminder? The key ideaShow

A square with all corners on a circle of radius $r$ has the area $2r^2$ . An equilateral triangle with all corners on the circle has the side $r\sqrt{3}$ and the area $\dfrac{3\sqrt{3}}{4}r^2$ . The leaf of two quarter circles of radius $a$ in a square of side $a$ is $\left(\dfrac{\pi}{2} - 1\right)a^2$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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