1. Unit 10: Measuring Length and Area By: Kylie Maxton & Seoyun Jang

2. Vocabulary for Unit 10 ★ Heron’s Formula: this is used to find the area of a triangle when given 3 side LENGTHS ★ Center of a polygon: center of circumscribed circle ★ Radius of a polygon: segment from center to vertice ★ Apothem of a polygon: perpendicular segment from the center to the side of a polygon ★ Central angle of a regular polygon: angle formed by 2 CONSECUTIVE radii

3. Key Concepts: Area Formulas Square, rectangle, parallelogram, rhombus : bh Circles: πr 2 Any triangle: ½ b*h a=apothem P=perimeter a Any regular polygon: ½aP Heron’s Formula: A=√s(s-a)(s-b)(s-c) s= a+b+c 2 Sector of a Circle: mAC * πr 2 360 Segment of a Circle: mAC * πr 2 -bh 360 2 A B C A C B Kite: ½(d 1 *d 2 ) Equilateral triangles: if side length of x, then A=x 2 √3 4 Trapezoid: ½(b 1 +b 2 )*h h b1b1 b2b2

4. Similar Figures: Ratios Ratio… of sides: X:Y of perimeters: X:Y of Areas: X 2 :Y 2 of Volumes: X 3 :Y 3

5. Key Concepts: Geometric Probability Probability: amount (area) of desired outcome every outcome (whole area) Find the area of the shaded piece if it’s an equilateral triangle and the circle has a radius of 6. Area - Area = Area of pink region A =½aP P=363 ½6*363=1083 A =36π Apink= 1083-36π 6

6. Common Mistakes ★ Mixing up and forgetting formulas-especially rhombuses and kites ★ Using the wrong segment for the apothem ★ Using Heron’s formula for the wrong type of triangles- remember, it can only be used when given side LENGTHS ★ Finding the apothem wrong ★ Correctly finding the geometric probability and subtracting/adding the wrong parts ★ Confusion between segments and sectors ★ Calculation errors and silly mistakes

7. 1515 1212 Easy: finding the area of a rectangle Area = base x height Area = 15 x 12 Area = 180

8. Medium: finding the segment of a circle To find the pink shaded region: ➔ mAC * πr 2 -bh 360 2 90° * 36π - 36 360° 2 ¼*36π-18 9π-18 = the area of the pink region ⌒ B A C □ 6

9. 360 5 Hard: area of regular polygon 72 36 54 8 4 6.8 4+?=6.8 16+?=46.24 ?=30.24=5.49 A=½aP A=½(5.5)(40) =½(220) A≈110

10. Real Life: Area of a Pizza Area = πr = π(20) = 400π = 1256 20 2 2

11. Units that Unit 10 Connects To ★ Unit 5: Similarity ○Similar figures and ratios are correlate with Area and Perimeter ★ Unit 7B: SohCahToa ○Sometimes SohCahToa is needed to find the measure of angles in regular polygons ★ Unit 11: Volume and Surface Area ○Proficiently finding area is needed in order to find volume and surface area