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JAMB Mathematics 2002 Question 30

Question 30

Mensuration of Plane Shapes

In the diagram above, XZ is the diameter of the circle XYZW, with centre O and radius 15/2cm. If XY = 12cm, find the area of the triangle XYZ.

Diagram for this question
  1. A.54cm2
  2. B.45cm2
  3. C.27cm2
  4. D.75cm2
Show the answer and explanation

Answer: A (54cm2)

Explanation

The angle in a semicircle is 90°, so ∠XYZ = 90° and XZ = 15 cm. Then YZ = √(225 − 144) = 9 cm, and the area is ½ × 12 × 9 = 54 cm2.