Question

the square and the rectangle have the dimensions shown. what description is true about the figures? a. same area, same perimeter b. same area, different perimeter c. different area, same perimeter d. different area, different perimeter

Explanation:

Step1: Calculate the area of the square

The area formula for a square is $A = s^2$, where $s$ is the side - length. For a square with $s = 8$ cm, $A_{square}=8\times8 = 64$ $cm^2$.

Step2: Calculate the perimeter of the square

The perimeter formula for a square is $P = 4s$. For a square with $s = 8$ cm, $P_{square}=4\times8=32$ cm.

Step3: Calculate the area of the rectangle

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. For a rectangle with $l = 12$ cm and $w = 4$ cm, $A_{rectangle}=12\times4 = 48$ $cm^2$.

Step4: Calculate the perimeter of the rectangle

The perimeter formula for a rectangle is $P=(l + w)\times2$. For a rectangle with $l = 12$ cm and $w = 4$ cm, $P_{rectangle}=(12 + 4)\times2=32$ cm.

Step5: Compare area and perimeter

The areas are different ($64
eq48$) and the perimeters are the same ($32 = 32$).

Answer:

B. same area, different perimeter