Question

On a square cardboard sheet of area 784 cm², four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

Answer 1

According to the question,

Area of the square = 784 cm²

∴ Side of the square = √Area = √784 = 28 cm

The four circular plates are congruent,

Then diameter of each circular plate = 28/2 = 14 cm

∴ Radius of each circular plate = 7 cm

We know that,

Area of the sheet not covered by plates = Area of the square – Area of the four circular plates

As all four circular plates are congruent,

We have, area of all four plates equal.

∴ Area of one circular plate = πr² = (22/7) × 7² = 154 cm²

Then,

Area of four plates = 4×154 = 616 cm²

Area of the sheet not covered by plates = 784 – 616 = 168 cm²