Area

The area is the size of a two-dimensional closed surface (the number of unit squares that cover the surface of the figure).

The area is measured in square units. We can use mm², cm², m², km², inches², yards², miles² or any other length square unit.

 

 

 

 

Area of a rectangle

We can find the area counting the number of square units.  The area of the following rectangle is 6 square units.

 

 

 

 

 

 

The number of unit squares in each row is the length of the rectangle.

The number of rows is the height of the rectangle

Area of the rectangle = length × height = 3 × 2 = 6 square units

Area of a parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides.

 

 

 

The base length is L and the distance between parallels is the height H.

 

 

 

 

 

 

We can transform a parallelogram into a rectangle, removing the right-angled triangle on the right and adding it on the left, as shown.

 

 

 

 

 

 

 

 

 

 

 

 

Always remember that length and height must meet at a right angle.

Area of the parallelogram = length × height

A rectangle has two diagonals (line segments linking opposite vertices)

Area of the triangle

A rectangle has two diagonals (line segments linking opposite vertices).

Each diagonal divides the rectangle into two congruent right triangles (each with half the area of the rectangle).

 

 

 

 

 

 

 

If we cut a rectangle in half diagonally we have two congruent right triangles.

The area of each triangle is  ½ length × height.

Also, if we cut a parallelogram in half diagonally we have two congruent triangles, as shown:

 

 

The area of each triangle is  ½ length × height.