Question 29 In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
First, let us find Area of Square
Given
Side of square ABCD = 14 cm
Area of square ABCD = (Side)2
= (14)2
= 196 cm2
Let us mark the shaded region as I , II, III, and IV.
Also,
Diameter of semicircle = Side of square = 14 cm
Radius of semicircle = 𝑆𝑖𝑑𝑒/2 = 14/2 = 7 cm
Area of semi circle AD = 1/2× area of circle
= 1/2×πr2
= 1/2×22/7 × (7)2
= 11 × 7
= 77 cm2
Since radius is same for semi-circle AD, BC, AB, CD
Area of all semi circles = 77 cm2
Area of region I + Area of region III
= Area of square ABCD
– (Area of semicircle AD + area of semi circle BC)
Area of region II + Area of region IV
= Area of square ABCD
– (Area of semicircle AB + area of semi circle 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) – (77 + 77 + 77 + 77)
= 200 – 4 × 77
= 392 − 308
= 84 cm2

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!