Question

OABC is a square inscribed
in a quadrant OPBQ.
If OA = 20 cm find the area of the shaded portion.
It's a challenge for Ravi​

Answer 1

ANSWER

ABCD is a square

OB = radius = r ( say)

we know angles of a square are 90 degree

and diognal of a square divide it into two equal right triangle

apply pythgourous thworem

r^2 = 2 ( 20 ) ^2

r ^2 = 800

r = √2 × 20 = 20√2

area of shaded region =

area of circle of radius r - area of square

4

=>π ( 800) / 4 - 20× 20

=> 400 × ( π/2 -1 ) cm^2

Answer 2

Answer:

228 cm^2

Step-by-step explanation:

area of square = side x side

                         = 20 x 20

                         = 400 cm^2

radius = OB

by Pythagoras theorem,

(OB)^2 = (AB)^2 + (OA)^2

(OB)^2 = 20 x 20 + 20 x 20

(OB)^2 = 400 + 400

OB = 10 x 2 x $\sqrt{2}$

radius  = 20$\sqrt{2}$

area of quadrant = 1/4 x pi x r^2

A = 1/4 x 3.14 x 20$\sqrt{2}$ x 20$\sqrt{2}$

A = 200 x 3.14

A = 628 cm^2

area of shaded portion = area of quadrant - area of square

area of shaded portion = 628 - 400

area of shaded portion = 228 cm^2

therefore area of shaded portion is 228 cm^2

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