EXAMPLE 1 Find angle measures in a regular polygon a. m AFB In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION.

Slides:

Advertisements

Similar presentations

EXAMPLE 2 Find the area of a regular polygon DECORATING

Advertisements

EXAMPLE 2 Find the area of a regular polygon DECORATING You are decorating the top of a table by covering it with small ceramic tiles. The table top is.

Section 11.6 Notes. Regular Polygon and its Parts.

11.2 Area of Regular Polygon

Areas of Regular Polygons and Circles

Sec. 10 – 3 Area of Regular Polygons

Regular Polygons A polygon is regular if all sides and interior angles are congruent. Congruent: same size, same shape.

Example 1 Explain how you could find the area of the regular hexagon shown.

FeatureLesson Geometry Lesson Main 1. Find the area of a trapezoid with bases 3 cm and 19 cm and height 9 cm. 2. Find the area of a trapezoid in a coordinate.

WARM UP 1)Find the area of a trapezoid with bases 8 and 11 and a height of )Find the area of an equilateral triangle with sides 8ft. 3)An isosceles.

Areas of Regular Polygons Lesson Equilateral Triangle Remember: drop an altitude and you create two triangles. What is the measure of the.

Area of Regular Polygons 5.5

Areas of Regular Polygons Honor’s On a sheet of warm up paper: Write the name of your podcast group members (don’t write your own name) Rate each.

1. An isosceles triangle has side lengths 20 meters,

10.3 Areas of Regular Polygons

9-2 Area of Regular Polygons The center of a regular polygon is equidistant from its vertices. Radius- the distance from the center to a vertex. Apothem-

11-5: Areas of Circles and Sectors 11-6: Areas of Regular Polygons Objectives: Find and apply the formula for the area of a circle. Find and apply the.

 Find areas of regular polygons.  Find areas of circles.  Bet ya didn’t see THAT coming!

Do- Now Do- Now  Warm UP  Go over Test  Review beginning slides from before break  TLW find areas of regular polygons and circles.

Geometry 10.5 Areas of Circles and Polygons Objectives Find the area of a circle and polygons To be able to solve problems with circles and polygons.

Section 12.3 Surface Areas of Pyramids and Cones.

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

Geometry Using Trig Functions to Find the Areas of Regular Polygons.

Areas of Regular Polygons Learning Target: I can use area to model and solve problems.

Areas of Regular Polygons Section Theorem 11.3 Area of an Equilateral Triangle: The area of an EQUILATERAL triangle is one fourth the square of.

10.3 Areas of Regular Polygons The radius of a regular polygon is the distance from the center to a vertex. The apothem is the perpendicular distance from.

Chapter 11.6 Notes: Areas of Regular Polygons Goal: You will find areas of regular polygons inscribed in circles.

Chapter 11: Measuring Length and Area Area of Regular Polygons.

10-3 Area of Regular Polygons. Radius of a regular polygon: the distance form the center to a vertex Apothem: the perpendicular distance from the center.

11.3 Areas of Regular Polygons and Circles What you’ll learn: 1.To find areas of regular polygons. 2.To find areas of circles.

Areas of Regular Polygons

Section 11-2 Areas of Regular Polygons. Area of an Equilateral Triangle The area of an equilateral triangle is one fourth the square of the length of.

Section 11-4: Areas of Regular Polygons and Composite Figures

Find the area of the triangle below. 3/24 with review 7.4 and 7.5 on 3/ Areas of Regular Polygons.

11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.

Warm Up Week 4. Section 11.2 Day 1 I will find the area of a regular polygon. Area of an Equilateral Triangle Theorem

11.5 Areas of Regular Polygons Objective: After studying this section you will be able to find the areas of equilateral triangles and other regular polygons.

Section 11-4 Areas of Regular Polygons. Given any regular polygon, you can circumscribe a circle about it.

 Given a regular polygon, you can find its area by dividing the polygon into congruent, non- overlapping, equilateral triangles.

Section 11.6 Area of a Regular Polygon. Homework Pg 765 #14-16, 19-21,

Agenda  1 st block  and triangle worksheet  Notes 11-4  Classwork due by end of class  3 rd block  Pop quiz  Go over homework.

Area of Regular Polygons January 27, Objectives Learn the formula for the area of regular polygons.

Geometry 11.6 Big Idea: Find Areas of Regular Polygons

CHAPTER 11.1 Angle Measures in Polygons. Sum of the Measures of the Interior Angles of a Convex Polygon… (n-2) * 180.

Areas of Regular Polygons. More... The apothem is the height of a triangle between the center and two consecutive vertices of the polygon. you can find.

Section 11.6: Areas of Regular Polygons Definitions – Given a regular polygon inscribed in a circle, the center and radius of the polygon is the center.

Area of Regular Polygons Terms Radius – segment joining the center of the polygon to the vertex of the polygon. All radii of a polygon are equal. When.

10-3 Areas of Regular Polygons. Parts of a Regular Polygon center radius apothem.

Regular Polygons radius – the distance from the center to a vertex We can center any regular polygon inside of a circle: Regular polygons: -all sides.

EXAMPLE 1 Find angle measures in a regular polygon a. m AFB In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION.

Areas of Polygons FORMULAS Rhombus: (1/2)d *d Kite: (1/2)d *d.

Area of Regular Polygons Regular – congruent sides and angles.

Area of Regular Polygons

1. An isosceles triangle has side lengths 20 meters,

Find the area of the triangle. POLYGONS Find the area of the triangle.

11.6 Areas of Regular Polygons

Areas of Polygons Section 11.3.

Today – Friday, June 7, 2013 Learning Target : You will find area of regular polygons inscribed in a circle. Independent practice BRING BOOKS ALL NEXT.

8.4 Areas of Regular Polygons

Calculate the size of the interior angles in a regular hexagon

11.5 Areas of Regular Polygons

Section 7.3 Regular Polygons and Area

All the polygons in this game are regular polygons.

Find x. Round to the nearest hundredth if necessary.

1. An isosceles triangle has side lengths 20 meters,

Areas of Regular Polygons

11.2 Areas of Regular Polygons

10-3 Areas of Regular Polygons

Using Trig Functions to Find the Areas of Regular Polygons

Section 7.3 More About Regular Polygons

Presentation transcript:

EXAMPLE 1 Find angle measures in a regular polygon a. m AFB In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION AFB is a central angle, so m AFB =, or 72 °. 360 ° 5

EXAMPLE 1 Find angle measures in a regular polygon b. m AFG In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION FG is an apothem, which makes it an altitude of isosceles ∆AFB. So, FG bisects AFB and m AFG = m AFB = 36 °. 1 2

EXAMPLE 1 Find angle measures in a regular polygon c. m GAF In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION The sum of the measures of right ∆GAF is 180 °. So, 90 ° + 36 ° + m GAF = 180 °, and m GAF = 54 °.

GUIDED PRACTICE for Example 1 In the diagram, WXYZ is a square inscribed in P. 1. Identify the center, a radius, an apothem, and a central angle of the polygon.

GUIDED PRACTICE for Example 1 SOLUTION center – P radius – PY or XP an apothem – PQ central angle – XPY

GUIDED PRACTICE for Example 1 2. Find m XPY, m XPQ, and m PXQ. m XPY is a central angle so m XPY = = XPQ = 45 ° SOLUTION m XPY = 90 ° QP is an apothem, which make it an altitude of isosceles ∆ XPQ so QP bisects XPY and m XPQ = m 1 2

GUIDED PRACTICE for Example 1 90 ° m PXQ = 180 and PXQ = 45 ° The sum of measures of right ∆ PXQ is 180° so