Multiple choice

From a piece of cardboard, in the shape of a trapezium ABCD, and AB$||$CD and $\angle$BCD$=90^o$, quarter circle is removed. Given AB$=$BC$=3.5$cm and DE$=2$cm. Calculate the area of the remaining piece of the cardboard.(Take $\pi$ to be $\dfrac{22}{7}$)

  1. $9.625cm^2$
  2. $6.125cm^2$
  3. $2.625cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Because AB and BC are 3.5 cm, the quarter circle has a radius of 3.5 cm, giving an area of one fourth times 22 over 7 times 3.5 squared, which equals 9.625 square cm. Since the trapezium has parallel sides of 3.5 and 5.5 cm and a height of 3.5 cm, its area is one half times 3.5 plus 5.5 times 3.5, or 15.75 square cm. Subtracting the circular area leaves 6.125 square cm of cardboard.

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