In the given figure square OABC is inscribed in a sector OPBQ. If OC = 20 cm, find the area of the shaded region (Use `pi = 3.14`)

Explanation

OC = CB = 20 cm
In right `Delta OCB`
`OB = sqrt(20^(2) + 20^(2))`
or `OB = 20 sqrt2`
`rArr` Radius of sector OPBQ `= 20 sqrt2 cm`
Area of sector `OPBQ = (pi r^(2) theta)/(360^(@)) = 3.14 xx (20 sqrt2)^(2) xx (90^(@))/(360^(@))`
`= (1)/(4) xx 3.14 xx 800 = 625 cm^(2)`
Area of square OABC `= 20^(2) = 400 cm^(2)`
Hence, the area of shaded region = Area of sector OPBQ - Area of square OABC
`628 cm^(2) - 400 cm^(2) = 228 cm^(2)`