Unit 10 Measuring Length and Area By Neeharika

Unit 10 Measuring Length and Area By: Neeharika and Jennifer

Area of Shapes Parallelogram Triangle A = ½*base*height A = base*height base₁ Square height A = base*height median Trapezoid A = (base₁ + base₂)/2*height A = median*height median = (base₁ + base₂)/2 base ₂ base l₁ na go A = base*height dia Rectangle al₂ base n go a i d Kite & Rhombus A = (diagonal₁ + diagonal₂)/2

Heron’s Formula and Equilateral Triangles Heron’s formula: √s(s-a)(s-b)(s-c) a b s=a+b+c 2 c s Equilateral triangle: √ 3 s 4

Ratio of Similar Figures ● ● Ratio of sides: a/b Ratio of perimeter: a/b Ratio of area: a^2/b^2 Angles congruent a b

Areas of Regular Polygons Area=1/2 a*p a=apothem a perimeter a a a

Area of Circles Sector: m∡A*πr^2 360 A=πr^2 Segment: sector-triangle Tri. r A r r

Geometric Probability P=area of desired outcome total area desired outcome

Common Mistakes ● ● ● Forgetting formulas Calculation errors Assuming info from diagrams (they’re not drawn to scale!) Not reading directions correctly Guess and check Basing answers off of previous answers

Connections to other Units ● Unit 7 a Right triangles and rules for right triangles are often used to find the measurements used to find the area of a figure. ● Unit 7 b Soh. Cah. Toa can be used to find values that are necessary to calculate the areas of figures. ● Unit 11 Finding the area of a figure is an important step in being able to find surface area, lateral area, and volume.

Real Life Situation -Someone who has to make a stop sign needs to find the correct measurements of the side lengths so that the sign will not be too big or small -They need to find the amount of material required to make it

Problems Easy: Find the area of this square 5 in Medium: Find the shaded area 6 in Hard: Find the probability of getting the shaded area 12 in

Solutions Easy: 25 in^2 (Area formula of square) Medium: 36π-27√ 3 in^2 (area of circle-area of triangle) Hard: 192π-288√ 3 in^2 ((A of circle-A of hexagon)/A of circle) 192π