Question

here is polygon q. what is the area of polygon q? lola drew a scaled copy of polygon q using a scale factor of 2. what is the area of lolas polygon? problems 10 - 11: spiral review

Explanation:

Step1: Divide the polygon into simpler shapes

Divide polygon Q into a rectangle and two right - triangles. The rectangle has length 3 units and width 2 units. The two right - triangles are congruent, with base 1 unit and height 2 units.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is $A_{rect}=l\times w$. Here, $l = 3$ and $w = 2$, so $A_{rect}=3\times2=6$ square units.

Step3: Calculate the area of one right - triangle

The area formula for a right - triangle is $A_{tri}=\frac{1}{2}\times b\times h$. Here, $b = 1$ and $h = 2$, so $A_{tri}=\frac{1}{2}\times1\times2 = 1$ square unit.

Step4: Calculate the total area of the polygon

Since there are 2 right - triangles and 1 rectangle, $A = A_{rect}+2\times A_{tri}$. Substitute the values: $A=6 + 2\times1=8$ square units.

Answer:

8 square units