HW 4.3(e) Due tomorrow: PW 11-4

HW 4.3(d) Solutions cm ft cm m, 40 m 10.a.6¾ in 2 b.4½ in, 3 in.

Guiding question: How is the area of regular & composite figures found?

Regular Polygons What is a regular polygon? A polygon with all sides congruent.

Parts of a Polygons You can circumscribe a circle about any regular polygon. Notice that since this is a hexagon, 6 congruent isosceles triangles are formed. The center of a regular polygon is the center of the circumscribed circle. The radius is the distance from the center to a vertex. The apothem is the perpendicular distance from the center to a side. TB pg 791 Guided Practice 1

Parts of a Polygons A central angle of a regular polygon has its vertex at the center of the polygon and its sides pass through consecutive vertices of the polygon. The measure of each central angle of a regular polygon is 360 n

Polygons The figure below is a regular pentagon with radii and an apothem drawn. Find the measure of each numbered angle. Notice that 5 congruent isosceles triangles are formed. So the 5 congruent angles at the center of the circle sum up to 360 o. Angle 1 = = 72 Angle 2 = ½ Angle 1 = 36 Angle 3 = 180 – 36 – 90 = 54

Polygons A portion of a regular hexagon has an apothem and radii drawn. Find the measure of each numbered angle.

Polygons Suppose you have a regular n-gon with sides s. The radii divide the figure into n congruent isosceles triangles. Each triangle has area… ½as The entire polygon then has area… n×½as The polygon has perimeter… ns So we can represent the area of any regular n-gon as… A = ½aP where ‘P’ is the perimeter and ‘a’ the apothem.

Polygons Find the area of a regular polygon with twenty 12-in sides and a 37.9 in. apothem. TB pg 793 Guided Practice 3A-C

Polygons A library is a regular octagon. Each side is 18.0 ft. The radius of the octagon is 23.5 ft. Find the area of the library to the nearest 10 ft. Find the area of an equilateral triangle with apothem 8cm. Leave your answer in simplest radical form.

Composite Figures A composite figure is a figure that can be separated into regions that are basic polygons. To find the area of a composite figure, find the area of the basic polygons and add them together.

Find the Area of the following: First find the missing lengths

Find the Area of the following: First find the missing lengths

Find the Area of the following: First find the missing lengths

Find the Area of the following: First find the missing lengths

Find the Area of the following: First find the missing lengths

Find the Area of the following: First find the missing lengths

Find the Area of the following: Spilt the figure into rectangles

Find the Area of the following: Spilt the figure into rectangles

Find the Area of the following: Rec. 1 area = 2 × 8 = 16 units 2 Rec. 2 area = 3 × 12 = 36 units 2 Rec. 3 area = 5 × 7 = 35 units 2 Area of figure = 87 units 2 TB pg 795 # 5 TB pg 794 Guided Practice 4A-B TB pg 794 Guided Practice 5A-B

Who wants to answer the Guiding question? How is the area of regular & composite figures found?