# 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)