Area of a Square
How to find the area of a square: formula, examples, and their solutions.
A = a2
A: area of a square
a = 4
A = 42
The square is a rhombus.
So the diagonals perpendicularly bisect each other.
So the brown segments are 3.
Diagonals of a rhombus
The bottom triangle is an isosceles right triangle.
So it's similar to a 45-45-90 triangle.
Draw a 45-45-90 triangle next to the given square.
The left triangle is × 3 bigger.
So the left triangle's hypotenuse is 3⋅√2.
a = 3√2
A = (3√2)2
There's another way to solve this example.
The square is a rectangle.
So the blue segments formed by the diagonals
are all congruent: 3.
Diagonals of a rectangle
The square is also a rhombus.
And the diagonals are 6 and 6.
So the area of the rhombus is (1/2)⋅6⋅6.