Question

Please solve the given question

Class 10
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Answer 1

☆Question☆

Find the area of the shaded region in the given figures

☆Answer☆

Given:-

• side of square =14cm
• Area of larger Square =side²=14 ²=196cm²

★There are four semi circle that means we have two complete circles of diameter of 2xcm

we know that,

3+x+2x+x+3=14

i.e., x=2

• so radius of circle is 2cm

Area of non shaded region=area of two circle + area of square of side 4cm

= 2πr ² +side²

= 25.12+16

= 41.12cm²

Therefore,

Required area of shaded region =196−41.12=154.88cm²

Answer 2

$\orange{\bold{Solution :-}}$

ar(sq ABCD) = (14× 14)cm²

Let the radius of each semicircle be a cm

then, (a+2a+a) = [14-(3+3)]cm = 8cm

∴4a = 8⇒a = 2cm

so,the radius of each semicircle =2

area of 4 semicircle =

$⟹(4 \times \frac{1}{2} \times 3.14 \times 2 \times 2) {cm}^{2}$

$⟹$$\blue{\bold{\boxed{25.12 cm² }}}$

length of each side of the smaller square

$⟶$ 2a cm

$⟶$(2×2)cm = 4cm

area of the smaller square = (4×4)cm²

= 16cm²

area of unshaded region = (25.12 + 16)cm² =41.12 cm²

Area of shaded region = (196-41.12)cm²

= 154.88 cm²

hence , the required area is 154.88 cm²