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 16𝑦𝑧 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. Let’s clear some space so we can
calculate this.
The area of rectangle A is 13𝑥
minus seven 𝑦𝑧. The area of rectangle B is two 𝑥
plus four 𝑦𝑧. And the area of rectangle C is
negative four 𝑥 plus nine 𝑦𝑧. The combined area is therefore as
shown. We can simplify this expression by
combining like terms. 13𝑥 plus two 𝑥 plus negative four
𝑥 is equal to 11𝑥. And negative seven 𝑦𝑧 plus four
𝑦𝑧 plus nine 𝑦𝑧 is equal to six 𝑦𝑧.
We can therefore conclude that the
combined area is equal to 11𝑥 plus six 𝑦𝑧. 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 16𝑦𝑧 minus five. This means that 13𝑥 minus seven
𝑦𝑧 plus the area of rectangle D must be equal to 16𝑦𝑧 minus five. Subtracting 13𝑥 and adding seven
𝑦𝑧 to both sides of this equation, we have the area of rectangle D is equal to
16𝑦𝑧 minus five minus 13𝑥 plus seven 𝑦𝑧.
Once again, we can combine like
terms. The area of rectangle D is equal to
negative 13𝑥 plus 23𝑦𝑧 minus five. This is the answer to the second
part of the question.
