Area and perimeter in the coordinate plane I

Find the perimeter and area of polygons graphed on a coordinate plane.

Lesson 2

Concept

To find the side lengths of a polygon on a coordinate plane, use the distance formula. For horizontal and vertical line segments, simply subtract the x- or y-coordinates. Then, use those side lengths to calculate area and perimeter.

Try it

A rectangle has vertices at (-2, 3), (4, 3), (4, -1), and (-2, -1). Find its area and perimeter.

Concept Check

A square has vertices at (0, 0), (0, 5), (5, 5), and (5, 0). What is its area?

Concept Check

What is the perimeter of a rectangle with vertices at (-1, 2), (-1, -3), (2, -3), and (2, 2)?

Steps to find area and perimeter

These steps are out of order — can you fix them?

1.Plot the given vertices on the coordinate plane

2.Find the lengths of the horizontal and vertical sides

3.Calculate perimeter by adding all side lengths

4.Calculate area by multiplying base times height

Short Answer

Why is it easiest to find the distance of horizontal or vertical line segments?

Coordinate Polygon Explorer

Drag the vertices to form a rectangle and observe how the side lengths affect area and perimeter.

Calculations

Perimeter

20units

Area

24sq units

Vertices

A(-2, 3)

B(4, 3)

C(4, -1)

D(-2, -1)

Drag the points around the coordinate plane grid to observe how lengths, perimeter, and area recalculate.