Find the area of the shaded …
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Sia ? 6 years, 6 months ago
Let the four shaded regions be denoted by I,II,III and IV as shown in the figure.
Given, side of square =10 cm
Diameter of each semi-circle =10 cm
Therefore, Radius of each semi-circle = {tex}\frac{10}{2}=5\;cm{/tex}
Now, area of I region + area of III region= Area of ABCD - Area of two semi-circles each of radius 5 cm
{tex}=(10\times 10-2\times \frac{1}{2}\pi \times 5^2){/tex}
{tex}=(100-3.14\times 25){/tex}
{tex}=100-78.5{/tex}
{tex}=21.5\;cm^2{/tex}
Similarly, area of II region + area of IV region = 21.5 cm2
Therefore, Area of the shaded region = Area of ABCD - Area of (I + II + III + IV) region
{tex}=(100-2\times 21.5){/tex}
{tex}=100-43{/tex}
{tex}=57\;cm^2{/tex}
The area of shaded design in the given figure is 57 cm2.
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