Hi im doing measurement at skool at the moment and i cant quite ork out some questions. Can someone please help!!
A chess board consists of 5cm squares of blackwood and maple(for the white squares) surrounded by an 8cm wide blackwood border. Determine th epercentage of the board which is made of maple.
do to you know geometry
Geometry : It is derived from an Arabic word genest which means figures.
Thus geometry means problems based on figures.
Sure, I'd be happy to help you with that!
To determine the percentage of the chessboard that is made of maple, we first need to find the area of the entire board and the area of the maple squares.
Let's break down the calculation step by step:
1. Calculate the area of a single blackwood square:
The blackwood squares are 5cm by 5cm, so the area of each blackwood square is 5cm × 5cm = 25cm².
2. Calculate the area of a single maple square:
Similarly, the maple squares are also 5cm by 5cm, so the area of each maple square is also 5cm × 5cm = 25cm².
3. Calculate the area of the blackwood border:
The blackwood border surrounds the board, and it has a width of 8cm. So, the border has a length of 8cm on all sides.
The overall dimensions of the board will be the length of a blackwood square plus two border widths: (5cm + 2 × 8cm) = 21cm.
Similarly, the overall width of the board will be 21cm.
Therefore, the area of the blackwood border is 21cm × 21cm = 441cm².
4. Calculate the area of the entire board:
The entire board is made up of the maple squares, blackwood squares, and the blackwood border.
Since there are 64 squares on a chessboard (8 rows × 8 columns), the area of the entire board is:
(64 maple squares × 25cm²) + (64 blackwood squares × 25cm²) + 441cm².
5. Calculate the percentage of the board made of maple:
Finally, to find the percentage of the board made of maple, divide the area of the maple squares by the total area of the board and multiply by 100.
Percentage = (Area of maple squares/Area of entire board) × 100.
Now, you can plug in the numbers and calculate the percentage.