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GEOMETRY

CHAPTER 3

Geometry & Measurement

3.1 Measuring Distance, Area and Volume 3.2 Applications and Problem Solving 3.3 Lines, Angles and Triangles

3.1 Rounding Example

2. First number to the right of 8 is “ 6 ”, so add one to 8
   4. Change all digits to the right to 0’s. The answer is, 39.00 or 39 Example: Round 38.67 centimeters to the nearest centimeter

3.1 Calculating Distances Linear Measure - a distance which could be around a polygon (perimeter) or around a circle (circumference) Perimeter - sum of the lengths of the sides C = π d (Re member d = 2 r ) Circumference - distance around circle

3.1 Metric Measures

1 cm = 0.01 m 1 dm = 0.1 m 1 mm = 0.001 m 1 hm = 100 m 1 km = 1000 m 1 dam = 10 m

3.1 Linear Distance

2. What is the distance around the polygon, in meters? 75 cm 78 cm 95 cm 80 cm 78 + 95 + 80 + 75 = 328 cm km A. 328 m hm dam m dm cm mm B. 32.8 m C. 3.28 m (^) D. 0.328m

3.1 Area - Square Units

4. What is the area of a circular region whose diameter is 6 cm? If d = 6, then r = 3

A = r

2 π Formula: = π (3) 2

D. 9 π sq. cm

A. 36 π sq. cm B. 6 π sq. cm

C. 12 π sq. cm

Surface area of a rectangular

solid

3.1 Examples of Area

L

W

H

There are 6 faces of the solid A=2LH Front/back Sides (Left/Right) +2WH Top/Bottom +2LW Square units

3.1 Volume - Cubic Units

Rectangular Solid Cylinder h h h (^) Cone Sphere V=lwh V = π r h 2 V r h 2 3 1 = π V = r 4 3 3 π r r r w l

3.1 Example of Volume

8. What is the volume of a sphere with a 12 inch diameter?

Formula: V = r

3 π If d = 12, then r = 6

V =

3

π ( ) Since (6)(6)(6)= 216 , the

only reasonable ans. is C

3.2 Application Example

1. What will be the cost of tiling a room measuring 12 ft. by 15 ft. if square tiles cost $2 each & measure 12 in.? Since 12 inches = 1 ft, one tile is 1 ft on each side or 1 sq. ft. Area room: A = bh; (12)(15) = 180 sq ft And (180)($2) = $360 cost A. $180 B. $4320^ C. $360^ D. $

3.2 Pythagorean Theorem For any RIGHT TRIANGLE c c a b 2 2 2 = + a b Side opposite the right angle is the hypotenuse “c”

3.2 Infer & Select Formulas

7. The figure shows a regular hexagon Select the formula for total area b Total area is the area of the 6 identical triangles. A. 3h+b If area of 1 triangle = 1/2xbh, then 6 x 1/2 x bh = 3 bh B. 6(h+b) C. 6hb D. 3hb h

3.3 Lines; Angles; Triangles

straight angle 180 right angle 90 obtuse > 90, < 180 acute angle < 90 comp. sum to 90 supp. sum to 180 vertical angles-equal

ANGLES TRIANGLES

Right triangle Acute triangle Obtuse triangle Scalene triangle Isosceles Equilateral