Question

A company manufactures circular-based chess pieces of a specific size, so that the round base of the pieces encompasses every square on the board. If each square has an area of 16 square cm, what is the area that the base of each chess piece must have?)

Answer 1

12.56 cm²

Step-by-step explanation

Given:

The area of the square = 16 cm²

What to find:

Area of the chess piece.

Step

The formula for an area, A of a square = L²

i.e A = L²

Since A is given to be 16 cm²

Therefore, the length is:

`\begin{gathered} A=l^2 \\ \\ 16cm^2=l^2 \\ \\ \Rightarrow l=√(16cm^2) \\ \\ l=4cm \end{gathered}`

Note that the length of the square is equivalent to the diameter of circular-based chess.

∴ D = 4 cm

Radius, r = D/2 = 4cm/2 = 2 cm

Area of the chess piece = πr²

Putting r = 2 cm and π = 3.14

Area of the chess piece = 3.14 x (2cm)² = 3.14 x 4cm² = 12.56 cm²