Question

What is the area of this polygon? Enter your answer in the box. units²

Answer 1

Answer:

The area of the polygon is $39\:units^2$

Step-by-step explanation:

Sketch the polygon to obtain the figure in the attachment.

The polygon can then be divided into a rectangle and a triangle.

The area of the polygon

$=|VE|\times |DE|+\frac{1}{2}\times |DE|\times |AM|$

We use the absolute value method to find the lengths

$=|3--2|\times |3--3|+\frac{1}{2}\times|3--3|\times |5-2|$

$=5\times 6+\frac{1}{2}\times 6\times 2$

$=30+9$

$=39\:units^2$

Answer 2

Answer:

The area of given polygon is 39 units² .

Step-by-step explanation:

It is given that the vertices of a 5-sided polygon on a coordinate plane are M(-5, 2), V(-2, 3), E(3, 3), D(3, -3) and R(-2,-3).

The composite figure has one rectangle and one triangle.

From the below figure it is clear that the length of the rectangle is 5 units and width of the rectangle is 6 units.

The area of a rectangle is

$A=length\times width$

$A_1=5\times 6=30$

The area of the rectangle is 30 units² .

From the below figure it is clear that the base of the triangle is 6 units and height of the triangle is 3 units.

The area of a triangle is

$A=\frac{1}{2}\times base\times height$

$A_2=\frac{1}{2}\times 6\times 3=9$

The area of the triangle is 9 units² .

The area of composite figure is

$A=A_1+A_2$

$A=30+9=39$

Therefore the area of given polygon is 39 units² .