Question

pls help with this question

Answer 1

We know that : Area of a Square is given by : Side × Side

Given : The Side of the Square as : 12 cm

⇒ Area of the given Square is : 12 × 12 = 144 cm²

Given : P , Q , R and S are the Midpoints of Sides AB - BC - CD - AD

⇒ Diameter of the Semi-Circles in Square is Half of the Side of the Square

⇒ Diameter of the Semi-Circle = 6 cm

⇒ Radius of the Semi-Circle = 3 cm

We know that : Area of Semi-Circle is given by : $\{\frac{\pi r^2}{2}\}$

⇒ Area of Semi-Circle : $(3.14\times\frac{9}{2}) = 14.13\;cm^2$

As there are 4 Semi-Circles :

⇒ The Total Area of the Semi-Circles = (4 × 14.13) = 56.52 cm²

We can Notice from the Diagram, Area of Shaded Portion will be :

⇒ Area of Square - Area of 4 Semi-Circles

⇒ Area of Shaded Portion : (144 - 56.52) = 87.48 cm²

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