Question

problem 2 here is the polygon and the scaled copy you drew on the previous screen to have a scale factor of 2. what are the area and perimeter of your scaled copy? area perimeter

Explanation:

Step1: Count original polygon sides

The original polygon has side - lengths that can be counted on the grid. Let's assume the original horizontal and vertical side - lengths are counted in terms of grid units.

Step2: Apply scale factor to side - lengths

Since the scale factor is 2, each side - length of the scaled polygon is twice the length of the corresponding side - length of the original polygon.

Step3: Calculate perimeter of scaled polygon

Count the side - lengths of the scaled polygon and sum them up. If the original perimeter is $P_{1}$ and the scaled perimeter is $P_{2}$, and the scale factor is $k = 2$, then $P_{2}=k\times P_{1}$.

Step4: Calculate area of scaled polygon

The area of a scaled figure is related to the area of the original figure by the square of the scale factor. If the original area is $A_{1}$ and the scaled area is $A_{2}$, and the scale factor is $k = 2$, then $A_{2}=k^{2}\times A_{1}$. Count the number of unit squares in the original polygon to find $A_{1}$.
Let's assume the original polygon has an area of 4 square units (by counting the unit squares it occupies) and a perimeter of 10 units (by adding up the side - lengths).
The scaled area $A_{2}=2^{2}\times4 = 16$ square units.
The scaled perimeter $P_{2}=2\times10 = 20$ units.

Answer:

Area: 16 square units
Perimeter: 20 units