Problem $2$

A $9-$inch$-$thick retaining wall with a complex shape will be constructed, and the contractor is ready to order the concrete. Given the dimensions shown on the following drawing $($dimensions are in fi$)$ you will determine the amount of concrete necessary to build the wall.

Use the coordinates given in the figure to create vectors $x$ and $Y$ that describe the top and the bottom borderlines of the wall. Y vector will be different for each border.

a$)$ Plot the coordinates given in the figure in a MATL.AB graph, plot should resemble the wall shaps.

b$)$ Use numerical integration, trapezoidal rule is an option, to estimate the area of the wall. Write the provedure for the trape$/$oidal rule on the live script file. Find the volume of the wall by multiplying the total area by the wall thickness.

c$)$ To improve the appearance of your plot and the area calculation try the following method in MATLAB, which generates more points for the borderlines using spline interpolation:d$)$ Use the trapezoidal rule to estimate the area of the wall using the new coordinates xp and y$.$ Find the volume multiplying the total area by the wall thickness. Compare with the result you oblained at $($c$).$