Question

here is polygon q. lola drew a scaled copy of polygon q using a scale factor of 2. what is the area of polygon q? what is the area of lolas polygon?

Explanation:

Step1: Divide the polygon into simpler shapes

We can divide polygon Q into 2 triangles and 1 rectangle. The rectangle has length 2 units and width 1 unit. Each triangle has base 1 unit and height 1 unit.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is $A = lw$. Here, $l = 2$ and $w=1$, so $A_{rectangle}=2\times1 = 2$ square - units.

Step3: Calculate the area of one triangle

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 1$ and $h = 1$, so $A_{triangle}=\frac{1}{2}\times1\times1=\frac{1}{2}$ square - unit.

Step4: Calculate the total area of the two triangles

Since there are 2 triangles, $A_{total - triangles}=2\times\frac{1}{2}=1$ square - unit.

Step5: Calculate the area of polygon Q

The area of polygon Q is the sum of the area of the rectangle and the total area of the two triangles. So $A = A_{rectangle}+A_{total - triangles}=2 + 1=3$ square - units.

Step6: Calculate the area of the scaled - copy

If the scale factor is $k = 2$, the ratio of the areas of two similar polygons is $k^{2}$. The area of the original polygon Q is $A_{1}=3$ square - units. The area of the scaled - copy $A_{2}=k^{2}A_{1}$. Substituting $k = 2$ and $A_{1}=3$, we get $A_{2}=2^{2}\times3=12$ square - units.

Answer:

The area of polygon Q is 3 square units. The area of Lola's scaled - copy of polygon Q (with a scale factor of 2) is 12 square units.