Question

what is the area of polygon q? lola drew a scaled - copy of polygon q using a scale factor of 3. what is the area of lolas polygon? explain your thinking.

Explanation:

Step1: Divide the polygon into simpler shapes

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

Step2: Calculate the area of the rectangle

The area formula for a rectangle is $A = l\times w$. Here, $l = 2$ and $w = 2$, so $A_{rectangle}=2\times2 = 4$ square units.

Step3: Calculate the area of the combined triangles

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

Step4: Calculate the total area of the polygon

The total area of polygon Q is the sum of the area of the rectangle and the area of the combined triangles. $A = A_{rectangle}+A_{triangles}=4 + 1=5$ square units.

Answer:

5 square units