Question

Help me with the 7 th question.

Answer 1

Hello,
we calculate the area of square:
A(ABCD)=L²=14²=196 cm²

given semicircle is drawn with side of square as diameter.
so, diameter of semicircles:
d=L=14 cm
we calculate the radius of semicircle:
r=d/2=L/2=14/2=7 cm

since radius is same for semi-cicle AD,AB,BC,CD.
we calculate the area the semi-cicle:
Ac=πr²/2=7²π/2=(49×3.14)/2=153,86/2=76.93 cm²

let us mark the unshaded region as a,b,c and d (see figure)
we calculate the area of region (a+b+c+d):
A(abcd)=2A(ABCD)-4Ac;
             =(2×196)-(4×76.93);
             =392-307.72=84.28 cm²

now, we calculate the area of shaded region:
A=A(ABCD)-A(abcd)=196-84.28=111.72 cm²

Hence area of shaded region is 111.72 cm²

bye :-)

Answer 2

Question-Find the area of the shaded portion in the given figure where ABCD is a square of side 14cm and semicircles are drawn with such side of square as diameter? 

Given- ABCD is a square in which each side is 14cm.
To find- The area of the shaded portion

Solution
Side of square ABCD = 14 cm
Area of square ABCD = 
$(side) {}^{2} = (14) {}^{2} = 196cm {}^{2}$
Given semicircle is drawn with side of square as diameter, 
So diameter of semicircle =Side of square =10cm
Radius of semicircle = 
$\frac{side}{2} = \frac{14}{2} = 7cm$

Area of semicircle AD =
$\frac{1}{2} \times area \: of \: circle = \frac{1}{2 } \times \pi \times r {}^{2}$
$\frac{1}{2} \times \pi \times (7) {}^{2} = \frac{3.14 \times 49}{2}$
Since radius is same for semi-circle AD, BC, AB, CD
Area of semi circle AD = Area of semi circle BC = Area of semi circle AB= Area of semicircle CD = 
$\frac{3.14 \times 49}{2}$

Let us mark the unshaded region as I, II, III and IV

Area of shaded region = Area of ABCD - (Area of I +II+III+IV) 

Area of region I +Area of region III
=Area of square ABCD - (Area of semicircle AD +Area of semicircle BC) 

Area of region II +Area of region IV
= Area of square ABCD - ( Area of semicircle AB +Area of semicircle CD) 

So, Area of region (I + II + III + IV )
=2 (Area of square ABCD) - (Area of semicircle AD + BC +AB +CD) 

Putting values

$2(196) - ( \frac{3.14 \times 49}{2} + \frac{3.14 \times 49}{2} + \frac{3.14 \times 49}{2}) \\ = 392 - 4 \times \frac{3.14 \times 49}{2 } \\ = 392 - 2 \times 3.14 \times 49 \\ = 392 - 307.72 \\ = 84.28 \: cm {}^{2}$

Now, Area of shaded region 
= Area of ABCD - (Area of I+II+III+IV) 
= 196 - 84.28
$111.72 \: cm {}^{2}$
Ans: Hence, the area of shaded region is 
$111.72 cm {}^{2}$

Hope, this solution helped you with 7th question 

-Ekansh Nimbalkar