Question

Read the following passage:

For the inauguration of 'Earth day' week in a school, badges were given to volunteers. Organisers purchased these badges from an NGO, who made these badges in the form of a circle inscribed in a square of side 8 cm. O is the centre of the circle and ∠AOB = 90°:

Based on the above information, answer the following questions:

1. What is the area of square ABCD?
2. What is the length of diagonal AC of square ABCD?
3. Find the area of sector OPRQO.
   OR
   Find the area of remaining part of square ABCD when area of circle is excluded.

Answer 1

i. Area of square ABCD = (Side)²,

= (8)²

= 64 cm²

ii. ΔABC, ∠B = 90°

∴ AC² = AB² + BC² = 2AB²

AC = `sqrt(2)  "AB"`

Diagonal AC = `8sqrt(2)  "cm"`

iii. Area of Sector OPRQO

= `θ/360 πr^2`

= `90^circ/360^circ xx 22/7 xx 4 xx 4  "cm"^2`

[Radius of inscribed circle = `1/2` side of square]

Area of sector OPRQO = `88/7`

= `12 4/7  "cm"^2`

OR

Area of circle = πr²

= `22/7 xx (4)^2`

= `352/7  "cm"^2`

∴ Required Area = `64 - 352/7`

= `(448 - 352)/7`

= `96/7  "cm"^2`

= `13 5/7  "cm"^2`