Area of a Rectangle: A shape consisting of several shapes (requiring the same formula)

Look at the rectangle below.

What is the area of the rectangle ABCD?

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AB=DC=8$

and also:

$BE=EC=2$

In other words, BC equals 4

Now we can find the area of the rectangle by multiplying the length by the width:

$AB\times BC=8\times4=32$

32 cm²

Look at the given rectangle made of two squares below:

What is its area?

In a square all sides are equal, therefore we know that:

$AB=BC=CD=DE=EF=FA=5$

The area of the rectangle can be found in two ways:

1. Find one of the sides (for example AC)

   $AC=AB+BC$

   $AC=5+5=10$

   and multiply it by one of the adjacent sides to it (CD/FA, which we already verified is equal to 5)

   $5\times10=50$

2. Find the area of the two squares and add them.

   The area of square BCDE is equal to the multiplication of two adjacent sides, both equal to 5.

   $5\times5=25$

   Square BCDE is equal to square ABFE, because their sides are equal and they are congruent.

   Therefore, the sum of the two squares is equal to:

   $25+25=50$

50

What is the area of the drawing shape?

Let's draw an imaginary line so that we get a shape with two rectangles, a large one and a small one.

Let's calculate the area of the large rectangle:

$14\times2=28$

Let's calculate the area of the small rectangle:

$1\times3=3$

Now let's combine them:

$28+3=31$

31 cm²