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AMO 2027 Grades 8-9 SET 15 - Self-study Question 2

AMO · AMO 2027 Grades 8-9 SET 15 - Self-study

Question 2

Exercise 14. The figure is made up of a semicircle and a right triangle. Given that the diameter of the semicircle is 42cm and the difference in area of region $A$ and region $B$ is $357\text{ cm}^2$, find the height of the triangle. Take $\pi=\frac{22}{7}$.

**Editorial input convention:** Use the pictured orientation: the area of A exceeds that of B by 357 square centimetres. The triangle base is the 42-cm semicircle diameter. Enter its perpendicular height in centimetres.

Question illustration