Areas, Surface Areas, and Volumes Unit

Slides:

Advertisements

Similar presentations

Honors Geometry Section 5.5 Areas of Regular Polygons

Advertisements

Area of Regular Polygons. We will determine the area of regular polygons using notes.

Section 11.6 Notes. Regular Polygon and its Parts.

Areas of Regular Polygons Students will be able to find the areas of regular polygons.

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

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

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.

11.5 Area of Regular Polygons. Theorem 106 Theorem 106: The area of an equilateral triangle equals the product of one- fourth the square of a side and.

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-

Areas of Regular Polygons Geometry Unit 4, Lesson 3.

11.4 Area of Regular Polygons

Lesson 8-4 Areas of Regular Polygons. In this lesson you will… ● Discover the area formula for regular polygons Areas of Regular Polygons.

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.

1 Geometry Section 6-3A Regular Polygons Page 442.

The Apothem The apothem (a) is the segment drawn from the center of the polygon to the midpoint of the side (and perpendicular to the side)

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.

You will be finding the area for a regular polygon. A regular polygon has all congruent sides and angles.

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.

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.

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

Chapter 10: Area Section 10-3: Areas of Regular Polygons.

Chapter 7 Lesson 5 Objective: Objective: To find the area of a regular polygon.

Polygons and Area (Chapter 10). Polygons (10.1) polygon = a closed figure convex polygon = a polygon such that no line containing a side goes through.

The area of the isosceles triangle is 31 in2. Find the perimeter.

Area and Perimeter Unit Area of 2-D Shapes.

AREAS OF REGULAR POLYGONS Geometry. Regular Polygons These are polygons with congruent sides and congruent angles. Apothem: A segment drawn from the center.

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 10-3 Areas of Regular Polygons Objectives: find area of a regular polygon Regular Polygon: equilateral and equiangular.

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.

6-3A Regular Polygons What are regular polygons? What is an apothem? How do you find the area of any regular polygon? How do you find the measure of one.

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

9.5 – Trigonometry and Area

Areas, Surface Areas, and Volumes Unit Areas of Regular Polygons.

Regular Polygons Finding Area.

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.

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.

Lesson 12-2 Pyramids (page 482) Essential Question How is the surface area and volume of pyramids different from prisms?

Area of Regular Polygons Regular – congruent sides and angles.

Area of Regular Polygons

Objectives Develop and apply the formula for the area of a regular polygon.

Lesson 12-2 Pyramids (page 482)

11.3 Volumes of Pyramids and Cones

May 1, 2017 Area of Regular Polygons

8.4 Areas of Regular Polygons

11.3 Areas of Regular Polygons and Circles

11.5 Areas of Regular Polygons

Section 7.3 Regular Polygons and Area

11.3 Vocabulary Radius of a Regular Polygon

LESSON 7.5 AREAS OF REGULAR POLYGONS OBJECTIVE:

11.3 Perimeters and Area of Similar Figures

side length: triangle:

Areas of Regular Polygons

Warm-Up#31 1. To estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree’s shadow end at the end point. Dave.

10-3 Areas of Regular Polygons

7.7 Perimeters and Area of Similar Figures

Using Trig Functions to Find the Areas of Regular Polygons

Areas of Regular Polygons

Area of Regular Polygons

8.4 Areas of Regular Polygons

10.3 Areas of Regular Polygons

11.3 Vocabulary Radius of a Regular Polygon

Presentation transcript:

Areas, Surface Areas, and Volumes Unit Areas of Regular Polygons

Things to Remember Trig Ratios : Angles of a Polygon Remember: 30-60-90 triangles shortcuts H = (SL ) 2 LL = ( SL )√ 3 Trig Ratios : Angles of a Polygon

Terms to Know: Any regular polygon: Radius: is a segment joining the center to any vertex Apothem: is a segment joining the center to the midpoint of any side and is also perpendicular to the side.

Area of a regular polygon: Remember all angles are congruent and all sides are congruent. N Regular pentagon: O is the center OA the radius OM is an apothem O T E P M A

Apothems Facts: All apothems of a regular polygon are congruent. Only regular polygons have apothems. An apothem is the perpendicular bisector of a side.

A reg. poly = ½ a p Where : a = apothem p = perimeter Area of a regular polygon equals one-half the product of the apothem and the perimeter. Where : a = apothem p = perimeter

A regular polygon has a perimeter of 40 cm and an apothem of 5 cm A regular polygon has a perimeter of 40 cm and an apothem of 5 cm. Find the polygon’s area. A = ½ap = ½(5)(40) = 100 cm2

Find the area of a regular hexagon whose sides are 18 cm long. Draw the picture Write the formula Plug in the numbers Solve and label units

A = ½ ap A = ½ (9√3)108 A = 486√3 cm 2 18cm P = 18(6) = 108 cm Find the perimeter Find each angle Find the apothem 18cm P = 18(6) = 108 cm Angles = 720º/6 angles = 120º per angle Radius breaks it into 60º angles. 30-60-90 triangle, apothem = 9√3 cm Write the formula, and solve. A = ½ ap A = ½ (9√3)108 A = 486√3 cm 2