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CHAPTER 2 KEY FORMULAS EQUATIONS

Line segments	Fig. 2.8	$\frac{a}{b} = \frac{c}{d}$ $\frac{a}{b} = \frac{c}{d}$ (2.1)
Triangle		$A = \frac{1}{2} b h$ $A = \frac{1}{2} b h$ (2.2)
Hero’s formula		$\begin{matrix} A = \sqrt{s (s - a) (s - b) (s - c)}, \\ where s = \frac{1}{2} (a + b + c) \end{matrix}$ $\begin{matrix} A = \sqrt{s (s - a) (s - b) (s - c)}, \\ where s = \frac{1}{2} (a + b + c) \end{matrix}$ (2.3)
Pythagorean theorem	Fig. 2.34	$c^{2} = a^{2} + b^{2}$ $c^{2} = a^{2} + b^{2}$ (2.4)
Square	Fig. 2.55	$A = s^{2}$ $A = s^{2}$ (2.5)
Rectangle	Fig. 2.56	$A = l w$ $A = l w$ (2.6)
Parallelogram	Fig. 2.57	$A = b h$ $A = b h$ (2.7)
Trapezoid	Fig. 2.58	$A = \frac{1}{2} h (b_{1} + b_{2})$ $A = \frac{1}{2} h (b_{1} + b_{2})$ (2.8)
Circle		$c = 2 π r$ $c = 2 π r$ (2.9)
		$A = π r^{2}$ $A = π r^{2}$ (2.10)
Radians	Fig. 2.84	$π rad = 180 °$ $π rad = 180 °$ (2.11)
Trapezoidal rule	Fig. 2.98	$A = \frac{h}{2} (y_{0} + 2 y_{1} + 2 y_{2} + \dots + 2 y_{n - 1} + y_{n})$ $A = \frac{h}{2} (y_{0} + 2 y_{1} + 2 y_{2} + \dots + 2 y_{n - 1} + y_{n})$ (2.12)
Simpson’s rule	Fig. 2.102	$A = \frac{h}{3} (y_{0} + 4 y_{1} + 2 y_{2} + 4 y_{3} + \dots + 2 y_{n - 2} + 4 y_{n - 1} + y_{n})$ $A = \frac{h}{3} (y_{0} + 4 y_{1} + 2 y_{2} + 4 y_{3} + \dots + 2 y_{n - 2} + 4 y_{n - 1} + y_{n})$ (2.13)
Rectangular solid	Fig. 2.112	$V = l w h$ $V = l w h$ (2.14)
		$A = 2 l w + 2 l h + 2 w h$ $A = 2 l w + 2 l h + 2 w h$ (2.15)
Cube	Fig. 2.113	$V = e^{3}$ $V = e^{3}$ (2.16)
		$A = 6 e^{2}$ $A = 6 e^{2}$ (2.17)
Right circular cylinder	Fig. 2.114	$V = π r^{2} h$ $V = π r^{2} h$ (2.18)
		$A = 2 π r^{2} + 2 π r h$ $A = 2 π r^{2} + 2 π r h$ (2.19)
		$S = 2 π r h$ $S = 2 π r h$ (2.20)
Right prism	Fig. 2.115	$V = B h$ $V = B h$ (2.21)
		$S = p h$ $S = p h$ (2.22)
Right circular cone	Fig. 2.116	$V = \frac{1}{3} π r^{2} h$ $V = \frac{1}{3} π r^{2} h$ (2.23)
		$A = π r^{2} + π r s$ $A = π r^{2} + π r s$ (2.24)
		$S = π r s$ $S = π r s$ (2.25)
Regular pyramid	Fig. 2.117	$V = \frac{1}{3} B h$ $V = \frac{1}{3} B h$ (2.26)
		$S = \frac{1}{2} p s$ $S = \frac{1}{2} p s$ (2.27)
Sphere	Fig. 2.118	$V = \frac{4}{3} π r^{3}$ $V = \frac{4}{3} π r^{3}$ (2.28) $A = 4 π r^{2}$ $A = 4 π r^{2}$ (2.29)
Frustum of right circular cone	Fig. 2.119	$V = \frac{1}{3} π h (R^{2} + R r + r^{2})$ $V = \frac{1}{3} π h (R^{2} + R r + r^{2})$ (2.30)
		$S = π (R + r) s$ $S = π (R + r) s$ (2.31)

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Table of Contents for CHAPTER 2 KEY FORMULAS EQUATIONS

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Table of Contents for
CHAPTER 2 KEY FORMULAS EQUATIONS