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Area and Perimeter of Plane Figures — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSArea and Perimeter of Plane Figures3 Marks
Question
The given figures show a rectangle $\text{ABCD}$ inscribed in a circle as shown alongside.
If $AB = 28 \ cm$ and $BC = 21 \ cm$, find the area of the shaded portion of the given figure.
✓

Answer

From the figure,
$AB = 28 \ cm$
$BC = 21 \ cm$
$ AC =\sqrt{ AB ^2+ BC ^2}$
$=\sqrt{28^2+21^2}$
$=35 .$
Hence diameter of the circle is $35 \ cm$ and hence
Area $=\pi \times\left(\frac{35}{2}\right)^2=962.5 \ cm ^2$
Area of the rectangle $= 28 \times 21 = 588 \ cm^2$
Hence area of the shaded portion is given by
$A = 962 - 588 = 374.5 \ cm^2​​​​​​​$​​​​​​​

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