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

figure: ar-a3-method.png A square tile has a side of 21 cm…

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

A square with side a. A circle inside it touches all four sides. The four corners of the square, which are outside the circle, are shaded orange. The circle is labelled circle and a corner is labelled corner. The side of the square is marked a with a double arrow. A caption says shaded equals square minus circle.

A square tile has a side of $21\ \text{cm}$ . A circle is painted on it and touches all four sides. Find the area of the unpainted corners, and the fraction of the tile that is unpainted. Take $\pi = \dfrac{22}{7}$ .

Need a reminder? The key ideaShow

Name the plain shapes. Add the pieces, or subtract the part that is cut away. Keep $\pi$ as a letter until the last step. The perimeter of a combined figure counts only its outer edge.

The worked solution

Have you tried it?

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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