Mid-Ordinate Rule \text { Area }=w\left(h_{m 1}+h_{m 2}+h_{m 3}+h_{m 4} \ldots+h_{m n}\right) W = width hm = Height of the mid ordinate Trapeziodal Rule \text { Area }=w\left(\frac{h_{1}+h_{n}}{2}+h_{2}+h_{3} \ldots+h_{n-1}\right) hHeight

of the ordinate w = width Simpsons Rule: For an even number of strips: \text { Area }=\frac{w}{3}\left(\text { (1st + last ordinate) }+\left(4 \times \sum \text { even ordinates }\right)+\left(2 \times \sum \text { odd ordinates }\right)\right) w = width Length of an arc = 2nR B/360; \text { Length of an arc }=2 \pi \mathrm{R} \beta / 360 ; \text { Long chords }=2 R \sin (\theta) \text { Tangent lengths = R tan ( } \beta / 2 \text { ); } \text { Tangential angles ( } \theta \text { ) }=(c / R) \times 90 / \pi Where R is the circular curve radius, B is the deviation angle and c is the chord length.