Here we will see how to establish the area of a rectangle and square, and look at the area of a square formula using the diagonal.
Area of a Square or Rectangle
The rectangle and the square are two of the most basic shapes in geometry.Working out the area of a rectangle or a square happens to be relatively straightforward when we know the length of the sides.
A standard square has a width and a height of the same length.
Area = WIDTH × HEIGHT
=> a × a or a2 This is the simplest area of a square formula.
Now for a standard rectangle.
Area = WIDTH × HEIGHT
=> a × b
The general differing values in height and width in a rectangle result in the different labels.
But the overall sum to perform is the same.
Examples
1.1
Area = 5cm × 5cm = 25cm2
1.2
What is the area of the following tennis court?
Solution
Area = WIDTH × HEIGHT
= 70m × 25m = 1750m2
1.3
If the area of a square is 36cm2.
What length are the sides of the square?
Solution
b2 = 36cm2
b = √36 = 6
Each side is 6cm in length.
1.4
If the area of the rectangle above is 45cm2.
What length is the width of the rectangle?
Solution
5 × w = 45 ( ÷ 5 )
w = \bf{\frac{\tt{45}}{\tt{5}}} => w = 9
The width of the rectangle is 9m.
1.5
The following image is the design of a door with 2 windows.
The wooden part is brown, with the glass parts light blue.
What is the total area of the wooden part of the door?
Solution
Total area of door including windows = 2m × 1.9m = 3.8m2
Area of 1 glass window = 0.6m × 0.8m = 0.84m2
Total window glass area = 2 × 0.84m2 = 1.68m2
Total door wooden area = 3.8m2 − 1.68m2 = 2.12m2
The wooden part of the door has an area of 2.12m2.
Area of a Square Formula, Diagonal
There is also another way to work out the area of a square, if you know the value of the length of the diagonal.
Area = \frac{d^2}{2}
Example
2.1
Area = \frac{6^2}{2} = \frac{36}{2} = 18
Area = 18cm2