Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

Slides:

Advertisements

Similar presentations

Area of Polygons and Circles

Advertisements

Areas of Regular Polygons 11.2 California State Standards 8 : Solve problems involving perimeter and area. 10: Find area of polygons 16: Perform constructions.

1.6 – Two-Dimensional Figures

Geometry 5 Level 1. Interior angles in a triangle.

Who Wants To Be A Millionaire?

Circle A is centered at (2,2) with a radius of 12 cm and Circle B is centered at (8,-2) with a diameter of 6 cm. Determine the translation and dilation.

Section 11.6 Notes. Regular Polygon and its Parts.

Geometric Constructions

Students will name two dimensional figures (9-4).

11.2 Area of Regular Polygon

Geometry Jeopardy Start Final Jeopardy Question Lines and Polygons Angles and More Naming Polygons TrianglesCircles Quadri- laterals

11.2a Area of Regular Polygons CCSSLESSON GOALS  Identify the radius, central angle, and apothem of a polygon.  Find the measure of a polygon’s central.

Perimeter Rectangles, Squares, and Triangles Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure,

The distance around the outside of a shape.

Geometry 11.4 Areas of Regular Polygons. Definitions Regular polygon- a polygon that is equiangular and equilateral. In the upper right side of your paper,

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

Rectangle l - length w - width Square s – side length s s s.

Introduction to congruent angles

10.3 Areas of Regular Polygons

Warm-Up What is the perimeter of a regular decagon with side length s = 6?

Geometry Chapter 11 Review. Solve for x Each exterior angle of a regular n-gon measures 40°. What is the value of n?

By. Circle Draw a circle in the box Tell about its attributes: sides, angles, whether or not it’s a polygon. Add any additional information you know about.

10/28/10 ©Evergreen Public Schools Area of Regular Polygons Vocabulary: apothem.

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.

9.4 Areas of Regular Polygons February 6, Definitions (associated with regular polygons only) Center of a polygon – the center of its circumscribed.

Area of regular polygons

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

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.

Chapter 11 Areas of Polygons and Circles

Circumference of a Circles

Geometry/Trig 2Name __________________________ Section 11-4 NotesDate _______________ Block ______ Regular Polygon:______________________________ _____________________________.

Circles, Polygons and Area WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

Angles-Polygons-Triangles- Quadrilaterals Angles If two lines cross we say they INTERSECT. If two lines in the same plane do not intersect, we say they.

Find the area of the equilateral triangle if one of the sides is 8.

Perimeter, Lines, & Angles

Area of regular polygons

11.2 Areas of Regular Polygons Unit IIIH Day 2. Do Now What are the two formulas for a 30º-60º-90º triangle? ▫hypotenuse = _________ ▫long leg = __________.

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.

Inscribed and Circumscribed Circles Dr. Jason Gershman.

Pythagorean Theorem, Perimeter, Circumference, Area ….

Perimeter, Circumference and Area. Perimeter and Circumference Perimeter : The distance around a geometric figure. Circumference: The distance around.

Perimeter The distance around the outside of a shape.

Lesson 4: Proving Area of a Disk STUDENTS USE INSCRIBED AND CIRCUMSCRIBED POLYGONS FOR A CIRCLE (OR DISK) OF RADIUS AND CIRCUMFERENCE TO SHOW THAT THE.

11.2 Areas of Regular Polygons Geometry. Find the area of the triangle below.

Areas of Regular Polygons Chapter 11, Section 2 June 22, 2016.

Lesson 11-4 Areas of Regular Polygons (page 440) Essential Question How can you calculate the area of any figure?

Area of Regular Polygons

Basic Geometric Terms.

1-8: Perimeter, Circumference, and Area

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

1.6 Two Dimensional Figures

Opener: How many diagonals does each polygon have

Area of Shapes.

8.4 Areas of Regular Polygons

Section 7.3 Regular Polygons and Area

9-2 Vocabulary Circle Center of a circle Center of a regular polygon

ACE problems Extension 17.

Geometry/Trig Name: __________________________________

10-3 Areas of Regular Polygons

Areas of Regular Polygons

Types of Polygons Tuesday, 07 May 2019.

Starter Which of these shapes has the greatest perimeter?

Lesson 11-3 Areas of Polygons.

Presentation transcript:

Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

The circle has a diameter of 1 unit. 1

This is the only piece of information you will be given, other than explanations of mathematical vocabulary. 1

What is the perimeter of the circumscribed square?

What is the perimeter of the inscribed regular hexagon?

What is the circumference of the circle?

What can you say about the perimeter of this regular inscribed octagon?

What can you say about the perimeter of the regular octagon, compared to the regular hexagon? Would you expect the perimeter of a regular, inscribed decagon to be greater or less than that of the octagon?

What would be the greatest length of the perimeter of an inscribed regular polygon, however many sides it has?

Generalising USING SYMBOLS

The circle has a diameter d. d

This is the only piece of information you will be given. d

What is the perimeter of the circumscribed square?

What is the perimeter of the inscribed regular hexagon?

What is the circumference of the circle?

Extension questions HIGHER TIER

Is the perimeter of the semicircle half the circumference of the circle?

What is the perimeter of the inscribed square, a) if the diameter of the circle is 1? b) if the diameter of the circle is d?

This time, the circle has a radius of 1 unit. 1

What is the perimeter of the inscribed equilateral triangle?

Some hints ADDING USEFUL LINES!

What is the perimeter of the inscribed regular hexagon?

What is the perimeter of the inscribed regular hexagon? We could add the diameter …

What is the perimeter of the inscribed regular hexagon? … but these are also diameters. What triangles are these? How do you know? What are the lengths of their sides?

What is the perimeter of the inscribed equilateral triangle?

What is the perimeter of the inscribed equilateral triangle? The radius of the circle may help …

… especially if we draw 3 of them …

… and project the lines … … to create other triangles whose angles we can deduce … … and whose side lengths we can calculate.