Answer: Area of the polygon 234
Step by step solution:
Let's start by naming each vertex of the polygon A(12,24), B(27,24), C(30,12) and D(6,12).
A and B have the same value of y = 24, AB is parallel to x-axis
C and D have the same value of y = 12, CD is parallel to x-axis
Then AB is parallel to CD
Measure AB = 27 - 12 = 15
Measure CD = 30 - 6 = 24
Since AB is not equal to CD, the polygon is a trapezoid, in a trapezoid the bases are parallel, and the other two sides are not parallel.
The area of a trapezoid can be calculated using the formula:
[tex]\begin{gathered} A=\frac{a+b}{2}\times h \\ A=\text{area} \\ a\text{ and b=bases} \\ h=\text{altitude (perpendicular distance from one base to the other)} \end{gathered}[/tex]
We have a = 15, b =24 and h = 24-12 = 12, plugin these values on the above formula.
[tex]\begin{gathered} A=\frac{15+24}{2}\times12 \\ A=234 \end{gathered}[/tex]
