PlaneGeometry_Basics_1-Perimeter-Area-Volume.pptx

Nociones de geometría plana. Cálculo de perímetro, área y volumen de figuras geométricas.

1. 1. Perimeter , Area and Volume

2. INTRODUCTION Geometry geos (meaning earth ) and metron (meaning measure ). S tudy of the properties of figures in the plane or space . The ancient Egyptians, Chinese, Babylonians, Romans, and Greeks used geometry for surveying, navigation, astronomy , and other practical occupations. The Greeks sought to systematize the geometric facts they knew by establishing logical reasons for them and relationships among them. Works of Tales, Pythagoras , Plato and Aristotles Elements (325 B.C, Euclid )

3. terms Point Line It has position only. It has no length, width, or thickness It has length, but has no width, or thickness. May be straight , curved or a combination of these Line Segment Side A line segment that is part of a geometric shape (figure) Vertex A point where two or more line segments meet

4. Plane It has length and width but no thickness Plane Figures Solid It has length, width and thickness Geometric Solids

5. Characteristics Sides are straight segments Sides only intersect at ends No curves Closed shape Polygon A flat , closed figure formed by three or more line segments joined at their ends.

6. Polygons Regular Irregular Has all its sides and angles equal Has unequal sides and angles

7. PolygoNS 3 8 10 5 6 4 12 7 Type of Polygon Number of sides 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 13 13 gon - n n - gon

8. Perimeter AND Area Perimeter ( P ) Distance around a figure (= the sum of its side lengths) Area ( A ) Amount of surface covered by a figure Circumference ( C ) Perimeter of a circle

9. Formulas for basic plane figures Square Side s P = 4 s A = s 2 s Rectangle Length (or height) h Width (or base) b P = 2 h + 2b A = hb h b Triangle sides a, b, c base b, height h P = a + b + c A = ½ bh a b c h Circle diameter d radius r C = 2 π r A = π r 2 d r  

10. UNITS OF MEASUREMENT PERIMETER Base unit (SI): meter ( m ) AREA Base unit (SI): squared meter ( m 2 )

11. EXAMPLEs 1. Find the perimeter and area of ​​a square with sides 11.3 m. 11.3 m       Perimeter Area       2. The area of ​​a rectangle is 6324 square centimeters. If the base measures 93 cm, what is the height? And what is its perimeter ?   93 cm ?       Area   Perimeter       s   A   b  

12. EXERCISES 1. Find the area of ​​a square whose perimeter measures 29.2 cm 2 . Find the perimeter of a square whose surface measures 10.24 square centimeters 3. The perimeter of a rectangle is 825 cm. If the base measures 125 cm, what is the height? 4 . How much will it cost to fence a square piece of land measuring 14 meters on a side if it costs 27 pesos per linear meter of wire? 5 . Painting a wall 8 m long and 75 dm wide cost 1140 pesos. What price was paid per square meter of paint?

13. 1 ) Calculate the perimeter and area of the following triangle . 2) Calculate the radius and area of ​​a circle whose circumference length measures 25.12 cm. 25.12 cm ?               Perimeter Area Perimeter Area               =(3.1416)(16 cm2)     EXAMPLEs

14. EXERCISES 1) Calculate the perimeter and area of the following triangles. 2 ) Find the areas of the shapes below

15. 3) Calculate the area and length (circumference) of a circle with a diameter of 6 meters. 4) Find the area of the semicircle below with a diameter of  8  centimeters . 5 ) Both circles share the same center. Find the  area of the shaded region.

16. ELEMENTS OF FIGURES PLANE SOLID

17. GEOMETRIC SOLIDS PLANE SOLID 2D 3 D BASIC TYPES

18. VOLUME Amount of space enclosed by a geometric solid

19. UNITS OF MEASUREMENT Liter   Metric units Cubic meter (m 3 ) *Base unit (SI): Liter (l) *Base unit : Capacity units

20. FORMULAS FOR BASIC SOLIDS

21. EXAMPLES 1) Express in cm 3 : a) 1 m 3 b) 5400 mm 3 c) 250 l   c )   a)   b)  

22. EXAMPLES 2 ) A swimming pool is 8m long, 6m wide and 1.5 m deep. The pool is painted at a rate of 120 pesos per square meter . a) How much will it cost to paint it? b) How many liters of water will be needed to fill it? a) We need to calculate the painted area in squared meters           Painted area   b) We need to calculate the volume of the pool and convert it lo liters   Volume of the pool      

23. EXERCISES 1) Express in m 3 a) b) 2 h m 3 c) 2) In a warehouse of dimensions 5m long, 3m wide and 2m high we want to store boxes of dimensions 10 dm long, 6 dm wide and 4 dm high. How many boxes can we store ? 3) Calculate the height of a prism whose base area is 1200 c m 2 and its capacity is 48 l. 4) A cylinder's height is the same length as the circumference of its base. And the height measures 125.66 cm . Calculate: a) The radio b ) The volume