Unit 10: Measurement, Area, Volume
by Nathaniel D'Amour
Areas of Parallelograms and Trapezoids
Parallelograms: A = bh
Trapezoids: A = 1/2(b1 + b2)h
Examples:
- Parallelograms:
- 57,800 = 680 * 85
- 571,500 = 635 * 900
- 57,956,250 = 7,025 * 8,250
- Trapezoids:
- 7,250 = 1/2 * (65 + 80) * 100
- 1,812.2 = 1/2 * (85 + 60) * 25
- 685,000 = 1/2 * (605 + 765) * 1,000
Areas of Circles
A = 3.14 * r^2
Examples:
- 31,400 = 3.14 * 100^2
- 9498.5 = 3.14 * 55^2
- 196,250 = 3.14 * 250^2
3-Dimensional Figures
- Prism (includes bases, vertices, and edges)
- Pyramid (includes bases, vertices, and edges)
- Cylinder (includes 1 base)
- Cone (includes 1 base)
- Sphere (includes 1 center)
Surface Area of Prisms & Cylinders
Prisms: S = 2B + Ph
Cylinders: S = (2* 3.14 * r^2) + (2 * 3.14 * r * h)
Examples:
- Prisms:
- 590 = (2 * 95) + (8 * 50)
- 700 = (2 * 65) + (95 * 6)
- 3,100 = (2 * (1/2 * 25 * 60)) + ((15 + 15+ 50) * 20)
- Cylinders:
- 1,909.12 = (2 * 3.14 * 8^2) + (2 * 3.14 * 6 * 30)
- 39,564 = (2 * 3.14 * 60^2) + (2 * 3.14 * 60 * 45)
- 770,085 = (2 * 3.14 * 75^2) + (2 * 3.14 * 75 * 1,560)
Surface Area of Pyramids & Cones
Pyramids: S = B + 1/2Pl
Cones: S = (3.14 * r^2) + (3.14 * r * l)
Examples:
- Pyramids:
- 3,500 = 1,500 + (1/2 * 40 * 100)
- 9,960 = 8,560 + (1/2 * 35 * 80)
- 15,665 = 5,815 + (1/2 * 20 * 985)
- Cones:
- 13,188 = (3.14 * 60^2) + (3.14 * 60 * 10)
- 137,375 = (3.14 * 70^2) + (3.14 * 70 * 555)
- 302,617.5 = (3.14 * 15^2) + (3.14 * 15 * 6,410)
Volumes of Prisms & Cylinders
Prisms: V = B = (l * w | 1/2 * l * w) * h
Cylinders: V = (B = 3.14 * r^2) * h
Examples:
- Prisms:
- 8,500 = (1/2 * 85 * 20) * 10
- 1,312,500 = (25 * 875) * 60
- 2,142,000 = (595 * 120) * 30
- Cylinders:
- 1,758.4 = (3.14 * 4^2) * 35
- 8,462.3 = (3.14 * 7^2) * 55
- 9,043.2 = (3.14 * 6^2) * 80
Volumes of Pyramids & Cones
Pyramids: V = 1/3 * (B^2 * h)
Cones: V = 1/3 * ((B = 3.14 * r^2) * h)
Examples:
- Pyramids:
- 2,083.4 = 1/3 * (25^2 * 10)
- 37,333.4 = 1/3 * (40^2 * 70)
- 74,666.7 = 1/3 * (80^2 * 35)
- Cones:
- 282.6 = 1/3 * ((3.14 * 3^2) * 30)
- 1,695.6 = 1/3 * ((3.14 * 6^2) * 45)
- 3,949.1 = 1/3 ((3.14 * 7^2) * 77)