Chapter 9 Big Ideas 9 1 Area formulas

Chapter 9 Big Ideas 9 -1: Area formulas of triangles and quadrilaterals: • Parallelograms • Triangles • Trapezoids • Quadrilaterals w/ diagonals (kite & rhombus) Find the area of each. A=½· d 1·d 2 A=½·h(b 1+b 2) 15 cm 12²+b²=15² 144+b²=225 b²=81 b=9 A=½· 12(9+18) A=6· 27 A=162 cm² 5 48 12 tan 48 = x/5 5 tan 48 = x x 5. 6 A=½· 10· 17. 5 A 87. 8 unit²

• 9 -2: Circles and Regular Polygons § Area and circumference of circles § Areas of regular polygons: (apothem and radius) Find the circumference of a circle whose area is 64 in² C=2 r C=2· 8· C = 16 in A = r² 64 = r² r² = 64 r=8 Find the area of the regular polygon. 360/(2· 8) =22. 5 A = ½·nsa A = ½· 8·(7. 6537)(9. 2388) A=282. 84 cm² 10 y x (Units are centimeters) sin 22. 5=x/10 10 sin 22. 5=x x 3. 8268 s 7. 6537 cos 22. 5=y/10 10 cos 22. 5=y y 9. 2388

9 -3/4: Composite figures and coordinate plane • Find areas by adding or subtracting known figures. • Estimating areas – Approximating a figure – Counting squares – (Pick’s Formula) • Finding area and perimeter of a figure on the coordinate plane. • Finding the area of a quadrilateral using subtraction. Estimate the area: 1 2 3 4 5 6 7 8 8 + ½ · 4 = 10 Find the area: A= ½bh + bh A= ½(7)(11. 2) + (5. 2) A= 36. 14 yd²

Find the perimeter and area of a figure with the vertices T(-4, 4), U(5, 3), V(4, -5), W(-5, 1) Perimeter: 3²+1²=c² 9²+1²=c² 82=c² 10=c² c= 82 c= 10 8²+1²=c² 65=c² c= 65 A = 10 · 9 ½· 1· 3 ½· 1· 9 ½· 8· 1 ½· 6· 9 A= 90 1. 5 4 27 A = 53 sq units 3 1 9²+6²=c² P= 10 + 82 + 65 + 117=c² P=31. 1 units c= 117 Area: Area of rect. - Area of 4 triangles 9 1 8 6 9 1

9 -5: Changing Dimensions • Non-proportional changes: Change in area is the product of the changes to the dimensions. • Proportional changes: Sides Perimeter Area m m m² 1. What happens to the area of a triangle whose base is doubled? Area is doubled 2. What happens to the area of a regular polygon whose sides are tripled? Area is 9 times bigger 3. You want to quadruple the area of a rectangular play area. Name three ways you could accomplish this. 4. Describe the change in area of a circle if its circumference is five times as big. Area is twenty-five times as big