1. A tract of land has a trapezoidal shape with two parallel sides a and b and the distance between them (i.etrapezoidal height) is h. You are given the following data:a = 125.42 m b = 208.84m h = 44.99mWrite the partial derivative equations of the area of the tract with respect to each of the two sides (a and b) andthe height (h). Compute the values of these partial derivatives using the data listed above. Make sure you listthe units for each computed partial derivative.

The solution is given below: Given a=125.42 m, b=208.84 m, h=44.99 mArea of a trapezoid is A=ha+b2, where a, b are the parallel sides and h is the height. The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Differentiate A with respect to a partially and evaluate the partial derivative for the given values of a=125.42 m, b=208.84 m, h=44.99 m . ∂A∂a=∂∂aha+b2 =∂∂aha2+hb2 =h2+0 =h2∂A∂a=44.992=22.495 m Differentiate A with respect to b partially and evaluate the partial derivative for the given values of a=125.42 m, b=208.84 m, h=44.99 m . ∂A∂b=∂∂bha+b2 =∂∂bha2+hb2 =0+h2 =h2∂A∂b=44.992=22.495 m Differentiate A with respect to h partially and evaluate the partial derivative for the given values of a=125.42 m, b=208.84 m, h=44.99 m . ∂A∂h=∂∂hha+b2 =a+b2∂A∂h=125.42+208.842=167.13 m