What is a square?
A square is a 2-dimensional (meaning flat) figure or shape, having four equal sides and each interior angle equal to 90°. It can be thought of as a rectangle with all sides equal. It has all general properties of a parallelogram. this article is on area of a square. It is worth listing down all the properties of a square:
- Opposite sides are parallel.
- All sides are equal.
- All interior angles are 90°.
- Diagonals are of equal length and bisect each other at right angles.
A square fits the definition of a quadrilateral, a parallelogram, a rectangle and a rhombus.
Area of a Square
Area is basically the quantity that expresses the measure of the extent of a 2-dimensional figure or shape. If the side of a square is given by ‘s’ then the formula of the area (A) is given by (s2).
Area of Square = side2
We also know that the side and diagonal of a square are related through famous Pythagoras Theorem.
If diagonal = d; then: s2 + s2 = d2
⇒ 2s2 = d2
⇒ A = s2 = d2 /2
Area of Square = (diagonal2)/2
Question 1: Find the area of a square of side 5 cm.
Solution: A square of side 5 cm would look like as shown aside. Formula for the area of a square is (side)2.
Hence, Area of square = 5 cm x 5 cm = 25 cm2
Question 2: Find the area of a square of side 16 cm.
Solution: Side of the square = s = 16 cm.
Area of the square = s2
= 162 cm2
= 256 cm2
Question 3: Find the length of the square whose area is 529 cm2.
Solution: Area of the square = A = 529 cm2
Side of the square = s = ?
Area of the square = A = s2
⇒ 529 cm2 = s2
⇒ s =
⇒ s = 23 cm
Hence the length of the side of this square is 23 cm.
Question 4: Find the area of the square whose diagonal is 16 cm.
Solution: Diagonal of the square = d = 16 cm.
Area of the square = d2/2
= 256/2 cm2
= 128 cm2
Question 5: Find the length of the diagonal of a square whose area is 32 cm2.
Solution: Area of the square = A = 32 cm2
Diagonal of the square = d = ?
Area of the square = A = d2/2
⇒ 32 cm2 = d2/2
⇒ d =
⇒ d = 8 cm
Hence the length of the diagonal of this square is 8 cm.
For area of a circle click here!