Question

The four points (−2, 5), (−2, −1), (7, −1), and (3, 5) are the vertices of a polygon. What is the area, in square units, of this polygon? 27 units2 33 units2 36 units2 42 units2

Answer 1

The area in square units of the given polygon is:

42 square units.

Explanation:

We know that the given vertices:

(−2, 5), (−2, −1), (7, −1), and (3, 5)

form the vertices of a polygon.

Also we know that the area of a trapezium with base length b and b' and height h is given by:

`Area=(1)/(2)* (b+b')* h`

From the figure we could see that:

b=9 units.

b'=5 units.

h=6 units.

Hence, the area of trapezium is given by:

`Area=(1)/(2)* (9+5)* 6\\\\\\Area=(1)/(2)* 14* 6\\\\\\Area=42`

Hence, the area of the trapezium is:

42 square units.