Question

spiral review
problems 10 - 11: here is polygon q.

1. what is the area of polygon q?

7 square feet units

1. lola drew a scaled copy of polygon q using a scale factor of 2. what is the area of lola’s polygon? explain your thinking.

reflection

Explanation:

Step1: Divide polygon Q into parts

We can divide polygon Q into a rectangle and two right - triangles. The rectangle has dimensions 2 units by 1 unit, and the two right - triangles can be combined to form a 1 - unit by 1 - unit square.

Step2: Calculate area of rectangle

The area of a rectangle is $A = l\times w$. For the rectangle in polygon Q with length $l = 2$ and width $w = 1$, $A_{rectangle}=2\times1 = 2$ square units.

Step3: Calculate area of combined triangles

The two right - triangles together form a square with side length $s = 1$. The area of a square is $A=s^{2}$, so $A_{triangles}=1\times1 = 1$ square unit.

Step4: Calculate area of polygon Q

The area of polygon Q, $A_Q=A_{rectangle}+A_{triangles}=2 + 1=3$ square units.

Step5: Calculate area of scaled polygon

If a polygon is scaled by a scale factor $k$, the ratio of the areas of the scaled polygon $A_{scaled}$ to the original polygon $A_{original}$ is $k^{2}$. Here, $k = 2$ and $A_{original}=3$ square units. So $A_{scaled}=k^{2}\times A_{original}=2^{2}\times3=12$ square units.

Answer:

1. 3 square units
2. 12 square units. The area of a scaled polygon is the square of the scale factor times the area of the original polygon. The original polygon Q has an area of 3 square units and the scale factor is 2, so $2^{2}\times3 = 12$ square units.