### Video Transcript

Consider three rectangles whose
areas are represented by the expressions below. All three rectangles are put
together such that none of them overlap. Write an expression to represent
the area of the new combined shape. If shape A is removed and instead
it sticks to a fourth rectangle, D, such that the shapes A and D do not overlap, the
combined area of A and D is 16π¦π§ minus five. Write an expression to represent
the area of rectangle D.

This question has two parts, and
the first part asks us to find the combined area of the three given rectangles. Since the rectangles do not
overlap, the area of the combined shape will be the sum of their areas. Letβs clear some space so we can
calculate this.

The area of rectangle A is 13π₯
minus seven π¦π§. The area of rectangle B is two π₯
plus four π¦π§. And the area of rectangle C is
negative four π₯ plus nine π¦π§. The combined area is therefore as
shown. We can simplify this expression by
combining like terms. 13π₯ plus two π₯ plus negative four
π₯ is equal to 11π₯. And negative seven π¦π§ plus four
π¦π§ plus nine π¦π§ is equal to six π¦π§.

We can therefore conclude that the
combined area is equal to 11π₯ plus six π¦π§. This is the answer to the first
part of this question.

In the second part of the question,
rectangle A is combined with a fourth rectangle, D. We are told that the combined area
of rectangles A and D is equal to 16π¦π§ minus five. This means that 13π₯ minus seven
π¦π§ plus the area of rectangle D must be equal to 16π¦π§ minus five. Subtracting 13π₯ and adding seven
π¦π§ to both sides of this equation, we have the area of rectangle D is equal to
16π¦π§ minus five minus 13π₯ plus seven π¦π§.

Once again, we can combine like
terms. The area of rectangle D is equal to
negative 13π₯ plus 23π¦π§ minus five. This is the answer to the second
part of the question.