Finding perimeter and area
Finding perimeter and area on the coordinate plane uses the coordinates of a polygon's vertices to calculate side lengths, then applies the appropriate formulas. For a rectangle with vertices at (1,1), (5,1), (5,4), and (1,4), the horizontal sides have length 4 and vertical sides have length 3, giving perimeter = 14 and area = 12. This Grade 7 math skill from Saxon Math, Course 2 integrates coordinate geometry with measurement formulas, preparing students for analytical geometry in Algebra and Geometry courses.
Key Concepts
Property By plotting the vertices of a polygon on the coordinate plane, we can determine the lengths of its sides and subsequently calculate its perimeter and area.
Examples A rectangle with vertices $(1, 1), (1, 2), (6, 2), (6, 1)$ has sides of length 5 and 3. The perimeter is the sum of all sides: $5+3+5+3=16$ units. The area is length times width: $5 \times 3=15$ square units.
Explanation Become a shape detective! Plot a shape's corners (vertices) on the grid. Count the squares between points to find the side lengths. Now you can easily calculate the shape's perimeter and area.
Common Questions
How do I find perimeter and area using coordinate plane points?
Find the length of each side using the coordinates (count units or subtract coordinates). Then apply the perimeter formula (sum of sides) and area formula for the shape.
How do I find the length of a horizontal or vertical segment on a coordinate plane?
For horizontal segments, subtract the smaller x-coordinate from the larger. For vertical segments, subtract the smaller y-coordinate from the larger. The result is the length.
Can I find the area of any polygon on a coordinate plane?
Yes. For rectangles and right triangles, use standard formulas with coordinate-calculated lengths. For irregular polygons, divide into rectangles and triangles, find each area, and add or subtract.
What is the area of a triangle on a coordinate plane?
Use A = (1/2) times base times height, where base and height are calculated from the coordinate differences. Alternatively, use the Shoelace Formula for any polygon on the coordinate plane.
When do students learn perimeter and area on the coordinate plane?
This topic is introduced in Grade 7. Saxon Math, Course 2 covers it in Chapter 9 as a connection between coordinate geometry and measurement.
How does coordinate plane area connect to the distance formula?
For slanted sides, the distance formula (square root of (x2-x1) squared + (y2-y1) squared) gives exact side lengths for use in perimeter calculations.
What are common mistakes when finding area on the coordinate plane?
Students sometimes use the diagonal distance where they should be using only the horizontal or vertical component, or forget to identify which points form the base and height.