POLYGONS

Polygon : a closed figure formed by coplanar line segments such that: − segments with a common endpoint are non-collinear − each segment intersects exactly two others and only at endpoints Polygons Not Polygons

Classifying Polygons Classifying polygons – a polygon is concave if, when any of the line segments are extended into lines, they pass through the interior of the polygon. The polygon looks as if it “caves in”. If none of the line extensions pass through the interior, the polygon is convex. Polygons

Classifying Polygons A convex polygon is said to be regular if all the sides are congruent and all of the angles are congruent. Regular Not Regular

Polygons A polygon is classified by the number of sides. Names exist for polygons up to 12 sides – beyond that we call them n-gons where n = number of sides. A list of these names is found on page 46 of our book. A polygon is named by listing the vertices in consecutive order.

Perimeter – the sum of the lengths of all sides of a polygon The perimeter of this flower bed would be = 19 m.

(Can also use the Pythagorean Theorem)

Example 6-1a Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular

Example 6-1b Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 9 sides, so this is a nonagon. A line containing some of the sides will pass through the interior of the nonagon, so it is concave. The sides are not congruent, so it is irregular. Answer: nonagon, concave, irregular

Example 6-1c Answer: triangle, convex, regular Answer: quadrilateral, convex, irregular Name each polygon by the number of sides. Then classify it as convex or concave, regular or irregular. a. b.

Example 6-2f SEWING Miranda is making a very unusual quilt. It is in the shape of a hexagon as shown below. She wants to trim the edge with a special blanket binding. The binding is sold by the yard. a.Find the perimeter of the quilt in inches. Then determine how many yards of binding Miranda will need for the quilt. Answer: 336 in., yd

Example 6-2f SEWING Miranda is making a very unusual quilt. It is in the shape of a hexagon as shown below. She wants to trim the edge with a special blanket binding. The binding is sold by the yard. b.Miranda decides to make four quilts. How will this affect the amount of binding she will need? How much binding will she need for this project? Answer:The amount of binding is multiplied by 4. She will need yards.

Example 6-3a Find the perimeter of pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1). 1)Count the squares to find the lengths of any sides that are horizontal or vertical. 2)Form right triangles for any other sides and use the Pythagorean Theorem to find their lengths – or use the distance formula for these.

Example 6-3b Answer: The perimeter of pentagon ABCDE is or about 25 units.

Example 6-4a The width of a rectangle is 5 less than twice its length. The perimeter is 80 centimeters. Find the length of each side. Let represent the length. Then the width is.

Example 6-4b Perimeter formula for rectangle Multiply. Simplify. Add 10 to each side. Divide each side by 6. Answer: The length is 15 cm. By substituting 15 for, the width becomes 2(15) – 5 or 25 cm.