Ex 12.3, 13
In figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π= 3.14)
Area of shaded region
= Area of quadrant OPBQ
– Area of square OABC
Area of square
Side of square = OA = 20 cm
Area of square = (side)2
= (20)2
= 20×20
= 400 cm2
Area of quadrant,
We need to find radius
Joining OB.
Also, all angles of square are 90°
∴ ∠ BAO = 90°
Hence, Δ OBA is a right triangle
Using Pythagoras theorem in Δ OBA
(Hypotenuse)2 = (Height)2 + (Base)2
(OB)2 = (AB)2 + (OA)2
(OB)2 = 202 + 202
(OB)2 = 400 + 400
OB2 = 800
OB = √800
OB = √(10×10×2×2×2)
OB = √(〖10〗^2×2^2×2)
OB = 10×2 √2
OB = 20√2
Hence, radius = OB = 20√2
Now area of quadrant = 1/4×𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒
= 1/4×𝜋𝑟2
= 1/4×3.14×(20√2 )2
= 1/2×3.14×(20×20×√2×√2 )
= 1/4×3.14×(400×2)
= 1/4×3.14×800
= 3.14 × 200
= 628 cm2
Now ,
Area of shaded region
= Area of Quadrant OPBQ – area of square OABC
= 628 – 400
= 228 cm2
Hence, area of shaded region = 288 cm2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.