Answer: 36 square centimeters
Step-by-step explanation:
To answer this question, we will find the area of the given figure. To do this, we will break the shape up into a few different parts. We see that there are two trapezoids and a square. Then, we will add all of these areas together.
The formula for the area of a trapezoid is:
A = [tex](\frac{b_1+b_2}{2}h )[/tex]
The formula for the area of a square is:
A = b²
Tile needed to create the pattern:
[tex]\displaystyle A=2(\frac{b_1+b_2}{2}h )+b^2[/tex]
[tex]\displaystyle A=2(\frac{(3)+(3+3)}{2}(6/2) )+(3)^2[/tex]
[tex]\displaystyle A=2(\frac{(3)+(6)}{2}(3) )+9[/tex]
[tex]\displaystyle A=2(\frac{9}{2}(3) )+9[/tex]
[tex]\displaystyle A=2(\frac{27}{2})+9[/tex]
[tex]\displaystyle A=27+9[/tex]
[tex]\displaystyle A=36\;square\;centimeters[/tex]
