Area of a Rectangle: Subtraction or addition to a larger shape

Look at the two rectangles in the figure:

What is the area of the white area?

As we know that EFGD is a rectangle, we also know that DE is equal to 2 and DG is equal to 4

In a rectangle, each pair of opposite sides are equal and parallel, therefore:

$ED=FG=2$

$DG=EF=4$

Now we calculate the area of the orange rectangle EFGD by multiplying the length by the width:

$2\times4=8$

Now we calculate the total area of the white rectangle ABCD:

$AD=AE+ED=2+2=4$

$DC=DG+GC=4+5=9$

The area of the entire rectangle ABCD is:

$4\times9=36$

Now to find the area of the white part that is not covered by the area of the orange rectangle, we will subtract the area of the rectangle EFGD from the rectangle ABCD:

$36-8=28$

28 cm²

The quadrilateral ABCD is a rectangle.

Points E and F are located on sides DC and BC respectively.

FC = 1.5 cm
EC = 5 cm
DE = 3 cm

AD = 4 cm

Calculate the area of the quadrilateral ABFE.

Let's calculate the side DC:

$3+5=8$

Now we can calculate the area of square ABCD:

$4\times8=32$

Let's calculate the area of triangle ADE:

$\frac{4\times3}{2}=\frac{12}{2}=6$

Let's calculate the area of triangle FCE:

$\frac{5\times1.5}{2}=\frac{7.5}{2}=3.75$

Now let's calculate the area of AEFB by subtracting the other areas we found:

$AEFB=32-6-3.75=22.25$

22.25

The shape below consists of a rectangle from which the line segment BH has been erased.

AB = 6 cm

AH = 7 cm

EF = 3 cm

HG = 12 cm

BC = 3 cm

Calculate the area of the shape shaded orange.

43.5 cm

Look at the rectangle in the figure.

A semicircle is added to each side of the rectangle.

What is the area of the entire shape?

$32+20\pi$ cm².