GEOMETRY WITH MR. REEVES 1.4 Perimeter and Area in the Coordinate Plane

1.4 Perimeter and Area in the Coordinate Plane

• Classify polygons • Find perimeters and

areas of polygons in the coordinate plane

VOCABULARY

WHAT YOU WILL LEARN

• polygon • side • vertex • n-gon • convex • concave

Vocabulary: Polygon, Sides, and Vertex

• In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure formed by three or more line segments called sides. Each side intersects exactly two sides, one at each vertex, so that no two sides with a common vertex are collinear.

• You can name a polygon by listing the vertices in consecutive order.

Naming Polygons

• The number of sides determines the name of a polygon.

Number of sides Type of polygon

3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon9 Nonagon10 Decagon12 Dodecagonn n-gon

• You can also name a polygon using the term n-gon, where n is the number of sides. For example, a 52-gon is a polygon with 52 sides.

Vocabulary: Convex and Concave

• A polygon is convex when no line that contains a side of the polygon contains a point in the interior of the polygon.

• A polygon is concave when there is a line that contains a side of the polygon and contains a point in the interior of the polygon.

Example 1

• Classify each polygon by the number of sides. Also, tell whether it is convex or concave.

Your turn…

• Complete Monitoring Progress #1-2 in your notebooks:

Perimeter and Area in the Coordinate Plane

• Whenever you are working with the coordinate plane, remember that you can use the Distance Formula to help with perimeter and area.

• Here are some helpful formulas that may look familiar for triangles, squares, and rectangles:

Example 2

• Find the perimeter of △ABC with vertices A(-3,4), B(-3,-1), and C(2,-1).

Your turn…

• Complete at least 2 problems from Monitoring Progress #3-6 in your notebooks:

Example 3

• Find the area of △DEF with vertices D(-3,-2), E(2,5), and F(4,-2).

Your turn…

• Complete at least 2 problems from Monitoring Progress #7-10 in your notebooks:

Example 4

• You are making a bumper sticker for a graphic design project. The four vertices of the bumper stick fall on the coordinate plane as shown. Each unit in the coordinate plane represents 2 inch. Find the area of the bumper sticker.

Your turn…

• Complete Monitoring Progress #11 in your notebooks:

Monitoring Progress Answers

1.4 Perimeter and Area in the Coordinate Plane

• Classify polygons • Find perimeters and

areas of polygons in the coordinate plane

VOCABULARY

WHAT YOU LEARNED

• polygon • side • vertex • n-gon • convex • concave