Polygons, Circles, and Solids

Slides:



Advertisements
Similar presentations
Working with Shapes in Two Dimensions
Advertisements

AREAS OF COMMON POLYGONS
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Using Formulas in Geometry
Using Formulas in Geometry
Using Formulas in Geometry
Mr. Barra Take The Quiz! Polygon with three edges (sides) and three vertices (corners) Sum of all interior angles equals 180° Right triangle One interior.
Perimeter Rectangles, Squares, and Triangles Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure,
 Write down objective and homework in agenda  Lay out homework (Graphing Picture)  Homework(Area Review)
3.2a: Surface Area of Prisms and Cylinders
Emily Reverman.  In this portfolio, you will see how to develop formulas for the area of different shapes (rectangle, parallelogram, trapezoid, and a.
FOR: MRS. GOODHUE’S CLASS BY: MRS. CAMUTO STUDY GUIDE FOR AREA, PERIMETER, VOLUME AND SURFACE AREA.
Perimeter & Area Section 6.1.
You will learn to solve problems that involve the perimeters and areas of rectangles and parallelograms.
Test Review Pay attention. What is the difference between area and perimeter? PERIMETER- – Distance AROUND the edge of a figure – Measures in regular.
Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved.
Target Apply formulas for perimeter, area, and circumference.
Area & Perimeter.
Area and Perimeter.
Surface Area of 12-3 Pyramids and Cones Warm Up Lesson Presentation
© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 9-3 Perimeter, Area, and Circumference.
Areas and Volume Area is a measure of the surface covered by a given shape Figures with straight sides (polygons) are easy to measure Square centimetres:
Section 9-4 Perimeter, Area, and Circumference.
Area & Perimeter Perimeter The distance around a shape – The sum of the lengths of all the sides in a shape – Measured in units of length i.e. Feet,
Area (geometry) the amount of space within a closed shape; the number of square units needed to cover a figure.
Rectangle The area of a rectangle is by multiplying length and height. The perimeter of a rectangle is the distance around the outside of the rectangle.
Section Using Formulas in Geometry Holt McDougal Geometry
Warm Ups Preview 10-1 Perimeter 10-2 Circles and Circumference
Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = c = 15, a = 9 3. b = 40, c = 41 4.
Geometry.
Areas of Parallelograms and Trapezoids. A parallelogram has two sets of parallel lines.
Jeopardy Geometry Circles 1 Triangles 2 Polygons 3 Formulas 4 Angles 5 Pot Luck
Objective Apply formulas for perimeter, area, and circumference.
Objective Apply formulas for perimeter, area, and circumference.
1.3 Using Formulas Geometry Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure, ADD the lengths.
Math More with Formulas 1. 2 Perimeter of a rectangle.
Perimeter - the distance around a figure 6 cm 4 cm You can find the perimeter of any polygon by adding the lengths of all its sides. 4 cm + 4 cm + 6 cm.
Warm-Up Find the area: Circumference and Area Circles.
1.7 Perimeter, Circumference, & Area
Definition: Rectangle A rectangle is a quadrilateral with four right angles.
Perimeter and Area January 24, Perimeter Example 1Find the Perimeter a. a square with a side length of 10 inches10 in. P = 4sPerimeter formula =
Warm Up Evaluate. Round to the nearest hundredth
WARM UP 11/30/15 Write down one fun thing that you did over Thanksgiving Weekend; turn to a neighbor and share 1.
Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = c = 15, a = 9 3. b = 40, c = 41 4.
To find the perimeter of a rectangle, just add up all the lengths of the sides: Perimeter = L + w + L + w         = 2L + 2w To find the area of a rectangle,
Perimeter, Lines, & Angles
Spring Board Unit 5 - Geometry.
Chapter 10 Geometry © 2010 Pearson Education, Inc. All rights reserved.
0-7: PERIMETER. 0-7: Perimeter  Perimeter: The distance around a figure. Perimeter is measured in linear units.
Perimeter, Circumference and Area. Perimeter and Circumference Perimeter : The distance around a geometric figure. Circumference: The distance around.
Geometry – Triangles and Trapezoids.  All Triangles are related to rectangles or parallelograms : Each rectangle or parallelogram is made up of two triangles!
Measurement. Introduction There are many different ways that measurement is used in the real world. When you stand on a scale to see how much you weigh,
9.1 PERIMETER AND AREA OF PARALLELOGRAMS Objective: Students find the perimeter and area of parallelograms.
Holt Geometry 1-5 Using Formulas in Geometry Warm Up Evaluate. Round to the nearest hundredth () 6. (3) 2.
G-11 (1-5) Using formulas in Geometry I can use formulas to compute perimeter and area of triangles, squares, rectangles, and circles.
Holt Geometry 11.4 Surface Area of Pyramids & Cones Learn and apply the formula for the surface area of a pyramid. Learn and apply the formula for the.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 1 Solving Application Problems 3.
7-9 Perimeter, Area, and Volume What You’ll Learn: To find the perimeter of polygons To find the perimeter of polygons To find the area of polygons/circles.
Name ____________Class_____ Date______ Area of Rectangles The ________ _ of a figure is the amount of surface it covers. It is measured in ________ __.
1-8: Perimeter, Circumference, and Area
11.3 Volumes of Pyramids and Cones
Perimeter Area and Circumference
Perimeter distance polygon sum sides Circumference length circle cm ft
Areas of Trapezoids, Rhombi, and Kites
Objective Apply formulas for perimeter, area, and circumference.
Area, Surface Area, Perimeter, Volume
Areas of Quadrilaterals and Triangles
Objective Apply formulas for perimeter, area, and circumference to composite figures.
Presentation transcript:

Polygons, Circles, and Solids Section 2.3 Polygons, Circles, and Solids

Common Polygons

Triangles

Quadrilaterals

Sum of Interior angles of Regular Polygon Interior sum of angles of regular polygon is (n-2)180, n is the number of sides What is the measure of the interior angles of a STOP sign? 1080 degree.

A rectangle has four sides that meet to form 90° angles A rectangle has four sides that meet to form 90° angles. Each set of opposite sides is parallel and congruent (has the same length). 90° angles In a rectangle, if one right angle is shown, the other three are also right angles. 5 cm 9 cm Each longer side of a rectangle is called the length (l) and each shorter side is called the width (w). Slide 8.3- 6

Slide 8.3- 7

Finding the Perimeter of a Rectangle Parallel Example 1 Finding the Perimeter of a Rectangle Find the perimeter of each rectangle. a. 6 m 16 m P = 2 • l + 2 • w P = 2 • 16 m + 2 • 6 m P = 32 m + 12 m P = 44 m The perimeter of the rectangle is 44 m. Slide 8.3- 8

Finding the Perimeter of a Rectangle Parallel Example 1 continued Finding the Perimeter of a Rectangle Find the perimeter of each rectangle. b. A rectangle 7.8 ft by 12.3 ft P = 2 • l + 2 • w P = 2 • 12.3 ft + 2 • 7.8 ft P = 24.6 ft + 15.6 ft P = 40.2 ft Or, you can add up the lengths of the four sides. P = 12.3 ft + 12.3 ft + 7.8 ft + 7.8 ft P = 40.2 ft Either method will give you the same result. Slide 8.3- 9

The perimeter of a rectangle is the distance around the outside edges. The area of a rectangle is the amount of surface inside the rectangle. 1 m 1 square meter or (m)2 8 m 5 m We have five rows of eight square meters for a total of 40 square meters. Slide 8.3- 10

Slide 8.3- 11

Other sizes of squares that are often used to measure area: Squares of many sizes can be used to measure area. For smaller areas, you might use the ones shown below. (Approximate-size drawings) 1 square inch (1 in.2) 1 in. 1 square centimeter (1 cm2) 1 cm 1 square millimeter (1 mm2) 1 mm Other sizes of squares that are often used to measure area: 1 square meter (1 m2) 1 square foot (1 ft2) 1 square kilometer (1 km2) 1 square yard (1 yd2) 1 square mile (1 mi2) Slide 8.3- 12

Finding the Area of a Rectangle Parallel Example 2 Finding the Area of a Rectangle Find the area of each rectangle. a. 7 yd 15 yd A = l • w A = 15 yd • 7 yd A = 105 yd2 Slide 8.3- 13

Finding the Area of a Rectangle Parallel Example 2 continued Finding the Area of a Rectangle Find the area of each rectangle. b. 18 cm 3 cm A = l • w A = 18 cm • 3 cm A = 54 cm2 Slide 8.3- 14

Slide 8.3- 15

Finding the Perimeter and Area of a Square Parallel Example 3 Finding the Perimeter and Area of a Square a. Find the perimeter of a square where each side measures 7 m. Use the formula. Or add up the four sides. P = 4 • s P = 7 m + 7 m + 7 m + 7 m P = 4 • 7 m P = 28 m P = 28 m Same answer Slide 8.3- 16

Finding the Perimeter and Area of a Square Parallel Example 3 continued Finding the Perimeter and Area of a Square b. Find the area of a square where each side measures 7 m. A = s2 A = s • s A = 7 m • 7 m A = 49 m2 Square units for area. Slide 8.3- 17

Finding the Perimeter and Area of a Composite Figure Parallel Example 4 Finding the Perimeter and Area of a Composite Figure a. The floor of a room has the shape shown. 6 ft 30 ft 21 ft 24 ft 15 ft Suppose you want to put new wallpaper border along the top of the walls. How much material do you need? Find the perimeter of the room by adding up the length of the sides. P = 30 ft + 21 ft + 24 ft + 15 ft + 6 ft + 6 ft = 102 ft Slide 8.3- 18

Finding the Perimeter and Area of a Composite Figure Parallel Example 4 continued Finding the Perimeter and Area of a Composite Figure b. The carpet you like cost $24.25 per square feet. How much will it cost to carpet the room? 6 ft 30 ft 21 ft 24 ft 15 ft Slide 8.3- 19

Finding the Perimeter and Area of a Composite Figure Parallel Example 4 continued Finding the Perimeter and Area of a Composite Figure Finally, multiply to find the cost of the carpet. 36+504= 540 sq feet. 6 ft 21 ft 24 ft Slide 8.3- 20

A parallelogram is a four-sided figure with opposite sides parallel, such as the ones below. Notice that the opposite sides have the same length. Slide 8.4- 21

Finding the Perimeter of a Parallelogram Example 1 Finding the Perimeter of a Parallelogram Find the perimeter of a the parallelogram. 15 cm 9 cm P = 15 cm + 9 cm + 15 cm + 9 cm = 48 cm Slide 8.4- 22

Slide 8.4- 23

Finding the Area of a Parallelogram Example 2 Finding the Area of a Parallelogram Find the area of the parallelogram. 10 m 4 m 3 m 4 m 10 m The base is 10 m and the height is 3 m. Use the formula to solve. A = b ∙ h A = 10 m ∙ 3 m A = 30 m2 Slide 8.4- 24

A triangle is a figure with exactly three sides A triangle is a figure with exactly three sides. To find the perimeter of a triangle, add the lengths of the three sides.

Finding the Perimeter of a Triangle Parallel Example 1 Finding the Perimeter of a Triangle Find the perimeter of the triangle. P = 12 ft + 16 ft + 20 ft = 48 ft 20 ft 12 ft 16 ft

Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2 it only works on Right Triangles. Where a and b are legs and c is the hypotenuse.

The height of a triangle is the distance from one vertex of the triangle to the opposite side (base). The height line must be perpendicular to the base; that is, it must form a right angle with the base.

Find the Area of a Triangle Parallel Example 2 Find the Area of a Triangle Find the area of each triangle. a.

Find the Area of a Triangle Parallel Example 2 continued Find the Area of a Triangle Find the area of each triangle. c.

r d Slide 8.6- 32

Finding the Diameter and Radius of a Circle Parallel Example 1 Finding the Diameter and Radius of a Circle Find the unknown length of the diameter or radius in each circle. a. Because the radius is 12 in., the diameter is twice as long. r = 12 in. d = ? d = 2 • r d = 2 • 12 in. d = 24 in. Slide 8.6- 33

Finding the Diameter and Radius of a Circle Parallel Example 1 continued Finding the Diameter and Radius of a Circle Find the unknown length of the diameter or radius in each circle. b. The radius is half the diameter. r = d 2 r = ? d = 7 m r = 7 m 2 1 2 r = 3.5 m or 3 m Slide 8.6- 34

The perimeter of a circle is called its circumference. Circumference is the distance around the edge of a circle. Slide 8.6- 35

Dividing the circumference of any circle by its diameter always gives an answer close to 3.14. This means that going around the edge of any circle is a little more than 3 times as far as going straight across the circle. This ratio of circumference to diameter is called Slide 8.6- 36

Slide 8.6- 37

Finding the Circumference of Circles Parallel Example 2 Finding the Circumference of Circles Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth. a. The diameter is 24 m, so use the formula with d in it. 24 m C = • d C = 3.14 • 24 m C ≈ 75.4 m Rounded Slide 8.6- 38

Finding the Circumference of Circles Parallel Example 2 Finding the Circumference of Circles Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth. In this example, the radius is labeled, so it is easier to use the formula with r in it. b. 6.5 cm C = 2 • • r C = 2 • 3.14 • 6.5 cm C ≈ 40.8 cm Rounded Slide 8.6- 39

Slide 8.6- 40

Finding the Area of Circles Parallel Example 3 Finding the Area of Circles Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. a. A circle with a radius of 14.2 cm. A = • r • r A ≈ 3.14 • 14.2 cm • 14.2 cm A ≈ 633.1 cm2 Rounded; square units for area Slide 8.6- 41

Finding the Area of Circles Parallel Example 3 continued Finding the Area of Circles Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. b. 24 ft First find the radius. r = d 2 r = = 12 ft 24 ft 2 Now find the area. A ≈ 3.14 • 12 ft • 12 ft A ≈ 452.2 ft2 Slide 8.6- 42

HW section 2.3 13-59