Question

3.2: representing areas
a
3
b
n
c
3
d
n + 1
e
n
1
f
n
match each figure with one or more expressions for its area. every shape that looks like a square is a square.

• (2 cdot 3^2)
• (6n^2)
• (n^2 + 1^2)
• (3^2)
• ((n + 1)(n + 1))
• ((2n)(3n))
• ((n + 1)^2)
• (3(3 + 3))
• (n^2)
• ((n + n)(n + n + n))
• (3^2 + 3^2)

Explanation:

for Figure A:

Step1: Identify the shape and dimensions

Figure A is a square with side length 3. The formula for the area of a square is side length squared.
So, Area = $3^2$. Also, $3^2 + 3^2$ is incorrect for A, but $3^2$ is correct. Also, $2\cdot3^2$ and $3(3 + 3)$ and $3^2+3^2$ relate to two squares of side 3, but A is one square. Wait, no, let's re - check. Figure A: square with side 3. Area = $3^2$.

Step2: Match with expressions

• $3^2$: Correct, as area of square with side 3 is $3\times3 = 3^2$.
• $3^2+3^2$ and $2\cdot3^2$ and $3(3 + 3)$: These are for two squares of side 3 (like Figure C). So Figure A matches with $3^2$.

for Figure B:

Step1: Identify the shape and dimensions

Figure B is a square with side length $n$. The formula for the area of a square is side length squared.
So, Area = $n^2$.

Step2: Match with expressions

• $n^2$: Correct, as area of square with side $n$ is $n\times n=n^2$.

for Figure C:

Step1: Identify the shape and dimensions

Figure C is a rectangle made up of two squares, each with side length 3. The length of the rectangle is $3 + 3=6$ and width is 3. Or we can think of it as two squares of area $3^2$ each.

• Area can be calculated as $2\times3^2$ (two squares of area $3^2$), or $3^2+3^2$ (sum of areas of two squares), or $3(3 + 3)$ (width 3, length $3 + 3$).

Step2: Match with expressions

• $2\cdot3^2$: Correct, since there are two squares with area $3^2$ each.
• $3^2 + 3^2$: Correct, sum of areas of two squares.
• $3(3 + 3)$: Correct, as area of rectangle is length×width = $3\times(3 + 3)$.

for Figure D:

Step1: Identify the shape and dimensions

Figure D is a square with side length $n + 1$. The formula for the area of a square is side length squared. So, Area=$(n + 1)\times(n + 1)=(n + 1)^2$. Also, $(n + 1)(n + 1)$ is the same as $(n + 1)^2$.

Step2: Match with expressions

• $(n + 1)(n + 1)$: Correct, as it's the area of a square with side $n + 1$.
• $(n + 1)^2$: Correct, same as above.

Answer:

s:

• Figure A: $3^2$
• Figure B: $n^2$
• Figure C: $2\cdot3^2$, $3^2 + 3^2$, $3(3 + 3)$
• Figure D: $(n + 1)(n + 1)$, $(n + 1)^2$
• Figure E: $n^2+1^2$
• Figure F: $6n^2$, $(2n)(3n)$, $(n + n)(n + n + n)$