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Assignment. P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35 P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48 Challenge Problems. Example 1. Explain how you could find the area of the regular hexagon shown. Regular Inscribed Polygon.

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**Assignment**• P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35 • P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48 • Challenge Problems**Example 1**Explain how you could find the area of the regular hexagon shown.**Regular Inscribed Polygon**The diagram shows a regular polygon inscribed in a circle. • Center of circle = center of the polygon • Radius of circle = radius of the polygon**Regular Inscribed Polygon**The apothem of the polygon is the distance from the center to any side of the polygon. • Apothem = height of isosceles triangle with 2 radii as legs**Regular Inscribed Polygon**A central angle of a polygon is an angle formed by two consecutive radii. • Measure of central angle =**11.6: Areas of Regular Polygons11.3: Perimeter and Area of**Similar Figures Objective: • To find the area of a regular n-gon • To describe the effects on perimeter and area when dimensions are changed proportionally**Example 2**• Identify the center, a radius, an apothem, and a central angle of the polygon. • Find m<XPY, m<XPQ, m<PXQ.**Example 3**Assume a regular n-gon has a side length of s and an apothem of a. Find a formula for the area of the regular n-gon.**Area of a Regular Polygon**The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P.**Regular 3-gon**What is the measure of each central angle in an equilateral triangle? What is the measure of the angle formed by the apothem and the radius of the triangle?**Regular 4-gon**What is the measure of each central angle in a square? What is the measure of the angle formed by the apothem and the radius of a square?**Regular 5-gon**What is the measure of each central angle in a regular pentagon? What is the measure of the angle formed by the apothem and the radius of the pentagon?**Regular 6-gon**What is the measure of each central angle in a regular hexagon? What is the measure of the angle formed by the apothem and the radius of the hexagon?**Example 4**Find the area of each regular polygon.**Example 5**Find the area of each regular polygon.**Example 6**Find the area of each regular polygon.**Example 7**Find a formula for the area of a regular hexagon in terms of s, the side length.**Example 8**The perimeter of a regular hexagon is 48 cm. What is the area of the hexagon?**Example 9**Find the area of the shaded region.**Example 10**Rectangle ABCD ~ PQRS with a scale factor of 3:4. Find the perimeter and area of rectangle PQRS.**Perimeter of Similar Polygons**If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their perimeters is a:b.**Area of Similar Polygons**If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a2:b2.**Example 11**In the diagram ΔABC ~ ΔDEF. Find the indicated ratio. • Ratio (red to blue) of the perimeters • Ratio (red to blue) of the areas**Example 12**Stuart is installing the same carpet in a bedroom and den. The floors of the rooms are similar. The carpet for the bedroom costs $117. Carpet is sold by the square foot. How much does it cost to carpet the den?**Example 13**The polygons below are similar. Find the values of x and y.**Assignment**• P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35 • P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48 • Challenge Problems

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