Ms. Ellmer Winter,

10-1: Areas of Parallelograms & Triangles Background: Once you know what a dimension does for you, you can take two dimensions and combine them for the Area. This is used in construction, landscaping, home improvement projects, etc. 2

10-1: Areas of Parallelograms & Triangles Vocabulary: Dimension: Measurement of distance in one direction. Area,A: Product of any 2 dimensions. Measures an object’s INTERIOR and has square units. Ex. m 2, cm 2, ft 2 Volume, V: Product of any 3 dimensions. Measures an objects INTERIOR PLUS DEPTH and has cubed units. Ex. m 3, cm 3, ft 3 Base: The side of any shape that naturally sits on the ground or any surface Height: The side of any shape that is to base. Parallelogram: A shape with 2 sets of parallel sides. NOTE: SLANTED SIDES ≠ HEIGHT 3

Ex.1 Label each side as a base or height or nothing. a. b. c. 10-1: Areas of Parallelograms & Triangles

Now that you can identify the base and height properly, now calculate the area of any shape. Use your formula sheet for the various formulas for shapes. Ex.2 Find the area of each triangle, given the base b and the height h. b = 8, h=2 A = ½∙(b∙h) A = ½∙(8∙2) A = : Areas of Parallelograms & Triangles 5

Ex. 3 What is the area of DEF with vertices D(-1,-5), E(4,-5) and F(4, 7)? Plot it on x-y coordinate system Connect dots. Count how long b is Count how long h is Use Area of Formula. A = ½∙(b∙h) A = ½*(5∙12) A = : Areas of Parallelograms & Triangles F D E 6

Now, you do ODDS 1-19 (skip 11) 10-1: Areas of Parallelograms & Triangles 7

What about weird shapes like trapezoids or kites? Kites/Rhombuses: Find area by finding the lengths of the two diagonals and plug into formula. Trapezoids: Find area by finding two bases and height using trig. functions : Areas of Trapezoids, Rhombuses, and Kites diagonal 1, d 1 diagonal 2, d 2 b2b2 b1b1 h

Ex.1 Find the area of each kite. A = ½d 1 ∙d 2 A = ½∙(9ft)(12ft) A = 54 ft : Areas of Trapezoids, Rhombuses, and Kites 6ft 9ft 6ft

Ex.1 Find the area of each trapezoid. First, find h with trig. functions. Tan(60°) = h/ = h h = 11.1 A = ½h(b 1 +b 2 ) A= ½(11.1)( ) A= in : Areas of Trapezoids, Rhombuses, and Kites 6ft 14.2 in in 60°

Now, you do EVENS : Areas of Trapezoids, Rhombuses, and Kites

10-5 Trigonometry and Area YOU DO ODDS

10-3 Area of Regular Polygons Background: Not all shapes are triangles, rectangles, and parallelograms. Think about your drive home: how many different shapes exist in the street signs you see? Vocabulary: Polygon: any shape with 3 or more sides. Center: the center of the imaginary circle that can be made on the outside of the polygon. Apothem: the height of the polygon. You find it by making an isosceles triangle and using trig functions or Pythagorean Theorem. Central Angle (CA)°: angle made from center to any vertex. CA° = 360°/nn = number of sides of polygon 13

10-3 Area of Regular Polygons How To Use It: Ex.1 Find the central angle of the following polygon. n = 8 CA° = 360° n 8 CA° =45° 14

10-3 Area of Regular Polygons How To Use It: Ex.2 Find the values of the variables for each regular hexagon. n = 6 CA° = 360° n 6 CA° =60° which is…which letter? b°! 15 4 d b° c

10-3 Area of Regular Polygons How To Use It: Ex.2 Find the values of the variables for each regular hexagon. To find c and d, you need Trig functions. First, bisect b° b° becomes 30° Now, go through trig recipe d 30° c 4

10-3 Area of Regular Polygons How To Use It: Tan (z°) = O A Tan (30°) = O = O 4 O = 2.31 But this is half of d, so d = d 30° c 4

10-3 Area of Regular Polygons How To Use It: Cos (z°) = A H Cos (30°) = 4 c = 4 1 c c = c = d 30° c 4

10-3 Area of Regular Polygons Vocabulary: Area of a Polygon: n A = ½∙a∙n∙s A = Area a = apothem n = number of sides s = length of side 19 a s

10-3 Area of Regular Polygons Now, you try ODDS

10-4 Perimeters and Areas of Similar Shapes Background: Sometimes, you don’t have all the dimensions of all sides for your shapes. So, if you know the perimeters or areas, you can make a proportion to figure it out. Vocabulary: Perimeter: Sum of all sides of any shape. The “outside” dimension. Area: The total amount of the “inside” of any shape. Proportion: Two ratios set equal to each other. 21

A 1 = a 2 A 2 b 2 P 1 = a P 2 b Perimeters and Areas of Similar Shapes a b

How To Use It: Ex.1 For each pair of similar figures, find the ratios of the perimeters and areas. P 1 = aA 1 = a 2 P 2 bA 2 b 2 P 1 = 4 A 1 = 4 2 P 2 3 A A 1 = 16 A Perimeters and Areas of Similar Shapes 3 4 4

Now, you do EVENS 2, 4, and 6 in 10 minutes! Perimeters and Areas of Similar Shapes

How To Use It: Ex.2 For each pair of similar figures, the area of the smaller shape is given. Find the missing area. A 1 = a 2 A 2 b 2 50 = 3 2 A (225) = A 2 (9) A 2 = 1250 in Perimeters and Areas of Similar Shapes A = 50 in 2 3 in 15 in

Now, you do EVENS 8-14 in 15 minutes! Perimeters and Areas of Similar Shapes

CH 10-6 Circles and Arcs Background: Circles have many measurements that can be taken: circumference, lengths of arcs, areas, diameters, and radii (plural for radius). 27 d

CH 10-6 Circles and Arcs Vocabulary: Circumference: Sum of the outside. C = π∙d Major arc: Distance GREATER than half of the circle Minor arc: Distance LESS than half of the circle Semicircle: Distance of half of the circle Measure of an arc (°): Central angles sum to 360°, and semicircle arcs measure 180 ° Length of an arc (cm, m, in): arc (°) ∙2∙π∙r 360(°) Diameter: a measure from end to end of a circle, passing through the center. Radius: Half of the diameter 28

CH 10-6 Circles and Arcs How To Use It: Ex. 1: Find the circumference of each side. Leave your answers in terms of π. r=12, so d=24 C = π∙d C = π∙24 C = 24π 29 12

Now, you do all, 1-3 in 5 minutes! Circle and Arcs

CH 10-6 Circles and Arcs How To Use It: Ex.2 State whether the following is a minor or major arc. BCD Minor arc 31 D A B C

CH 10-6 Circles and Arcs Now, you do 4-9 in 5 minutes! 32

CH 10-6 Circles and Arcs How To Use It: Ex.3 Find the measure of each arc in the circle. DAB °=? ACD = 180° AB = 180°-70° AB = 110° DAB = ACD + AB DAB = 290° 33 D A B C 70°

CH 10-6 Circles and Arcs Now you do 16,18,20 34

CH 10-6 Circles and Arcs Ex. 4 Find the length of each arc. BD = ? Length BD = mBD ∙2∙π∙r 360 Length BD = 90 ∙2∙π∙ Length = 0.25∙26 ∙π BD = 6.5 π 35 D A B 26 in

CH 10-6 Circles and Arcs Now you do 21,22,and23 36

CH 10-7 Areas of Circles and Sectors Vocabulary: Area of a Circle: A = π∙r 2 Area of a Sector of a Circle: Asector = arc (°) ∙π∙r 2 360(°) 37

CH 10-7 Areas of Circles and Sectors Ex. 1 Find the area of the shaded segment. Leave your answer in terms of π Areasector = mBD ∙π∙r Areasector= 90 ∙π∙ Areasector = 0.25 ∙π∙64 Areasector = 16π 38 D A B 8 in

CH 10-7 Areas of Circles and Sectors Now you do ODDS

YAHOO!!!!!!! We’re done with CH10! 40