Question

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

5-sided polygon on a coordinate plane with points M, V, E, D, and R. Point M is at (negative 5, 2), point V is at (negative 2, 3), point E is at (3, 3), point D is at (3, negative 3), and point R is at (negative 2, negative 3).

Answer 1

To find the area of the given 5-sided polygon, apply the Shoelace formula using the vertices' Cartesian coordinates. After performing the necessary calculations, the area is determined to be 33 units².

Step-by-step explanation:

To calculate the area of a 5-sided polygon on a coordinate plane with the given vertices, we use the technique of decomposing the polygon into smaller, non-overlapping triangles. Or, we use the Shoelace formula which is a method to determine the area of a polygon whose vertices are given in the Cartesian coordinate system.

The Shoelace formula states that the area of the polygon is:

• Calculate the sum of the product of the x-coordinates of each point by the y-coordinate of the point immediately following it.
• Calculate the sum of the product of the y-coordinates of each point by the x-coordinate of the point immediately following it.
• Subtract the second sum from the first sum.
• Take the absolute value of the result and divide by 2 to get the area.

Applying this formula to the provided coordinates:

• area = |([(–5)(3) + (–2)(3) + (3)(–3) + (3)(–3) + (–2)(2)] - [((2)(–2) + (3)(3) + (3)(3) + (–3)(–5) + (–3)(2)])| / 2
• area = |[(–15) + (–6) + (–9) + (–9) + (–4)] - [(–4) + 9 + 9 + 15 + (–6)]| / 2
• area = |(–43) - 23| / 2
• area = |–66| / 2
• area = 33 units²

Answer 2

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|* |DE|+(1)/(2)* |DE|* |AM|`

We use the absolute value method to find the lengths

`=|3--2|* |3--3|+(1)/(2)*|3--3|* |5-2|`

`=5* 6+(1)/(2)* 6* 2`

`=30+9`

`=39\:units^2`