To calculate the area of a square, in addition to the formula S = a2 where a is the side length, you can also find the area of a square when you know the diagonal or perimeter.
What is a square?
A square is a special quadrilateral in plane geometry with four equal sides and four right interior angles.
Formula for calculating the area of a square
According to the textbook Connecting knowledge with life, Math 3, volume 2, lesson 52, to calculate the area of a square, we take the length of one side and multiply it by itself.
| S = axa = a 2 |
In there:
S: Area of the square
a: Length of one side of a square
Example: Calculate the area of a square with each side length 3cm
Answer: The area of the square is S = 5 x 5 = 52 = 25 (cm 2 )
Formula for calculating the area of a square through the diagonal
The property of a square is that it has two diagonals of equal length, intersecting at right angles at their midpoints. The diagonals will divide the square into two equal right triangles.
According to the formula for calculating the area of a triangle, it is ½ the base multiplied by the height perpendicular to this base, where the base is the diagonal and the height is ½ the diagonal, so the area of the square will now be equal to:
| S = 2 x (dx ½ d) = d 2 /2 |
Example: Calculate the area of a square with a diagonal length of 10m
Answer: The area of the square is: S = 2 x (10 x ½ 10) = 10 2 /2 = 50 (m 2 )
Is a square a rectangle?
Yes, a square is a special rectangle. A square has all the properties of a rectangle: 4 right interior corners, 2 pairs of opposite sides are parallel and equal, the only difference is that a square has all sides equal and has perpendicular diagonals.
Compare square and rectangle
| Properties | Square | Rectangle |
|---|---|---|
| All sides are equal | Have | Are not |
| Opposite sides are equal | Have | Have |
| Parallel opposite sides | Have | Have |
| All angles are equal | Have | Have |
| Opposite angles are equal | Have | Have |
| The sum of two adjacent angles is 180 degrees | Have | Have |
| Equal diagonals | Have | Have |
| Diagonals intersect at midpoint | Have | Have |
| Perpendicular diagonal | Have | Are not |
Is a square a parallelogram?
Yes, a square is a special type of parallelogram. A square has all the properties of a parallelogram such as two pairs of opposite sides being parallel and equal. The special thing is that a square has four right angles and four equal sides.
Yes, a square is a special type of rhombus. A square has all the properties of a rhombus such as having four equal sides and opposite sides parallel. The special thing is that a square has additional right angles and two equal diagonals.
Compare square and rhombus
| Properties | Square | Diamond |
|---|---|---|
| All sides are equal | Have | Have |
| Opposite sides are equal | Have | Have |
| Parallel opposite sides | Have | Have |
| All angles are equal | Have | Are not |
| Opposite angles are equal | Have | Have |
| The sum of two adjacent angles is 180 degrees | Have | Have |
| Equal diagonals | Have | Are not |
| Diagonals intersect at midpoint | Have | Have |
| Perpendicular diagonal | Have | Have |
