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Mensuration — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMensuration4 Marks
Question
In the figure given below, ABCD is the rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle. (Take $\left.\pi=\frac{22}{7}\right)$.
✓

Answer

Considering the given figure:

Given dimensions of the rectangle: AB = 14 cm and BC = 7 cm
⇒ Radius of the quarter circle = 7 cm
Area of the quarter circle
$=\frac{1}{2} \times \frac{22}{7} \times 7^2 \text { sq. } cm$
$=\frac{77}{2} sq . cm $
Since EC = 7 cm and DC = 14 cm, we have
Therefore, radius of the semi circle = $\frac{7}{2} cm$
Area of the semi circle $=\frac{1}{2} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^2$ sq. $cm$
$=\frac{77}{4}$ sq. $cm$
Now, are of rectangle ABCD = AB x BC = 14 x 7 = 98 sq. cm
∴ Required area = Area of rectangle ABCD - [Area(BCEF) + Area(DGE)]
$=98-\frac{77}{2}-\frac{77}{4}$
$=\frac{161}{4}$
$=40.25 \text { sq. } cm $

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