Question

Ythe vertices of the polygon are (12,24), (27,24), (30,12) , (6,12) find the area of the polygon

Answer 1

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:

`\begin{gathered} A=(a+b)/(2)* h \\ A=\text{area} \\ a\text{ and b=bases} \\ h=\text{altitude (perpendicular distance from one base to the other)} \end{gathered}`

We have a = 15, b =24 and h = 24-12 = 12, plugin these values on the above formula.

`\begin{gathered} A=(15+24)/(2)*12 \\ A=234 \end{gathered}`