IEAS 36. Graph the astroid x = a 60536, y = a sin36 and set up an integral for the area that it encloses. Then use a computer algebra system to evaluate the integral. The equations given to you are given in parametric form. The easiest way to plot this in Mathematica is via the ParametricPlot command. The "a" here is a constant. For your picture, pick a constant; I've chosen "2" for my example code: The command ParametricPlotH2 (Cos [t] ) A3,2 (Sin[t] ) A3} , (t, 0,2Pi}] will plot the correct shape (I went t from 0 to 2Pi because I wanted "one full rotation" for the trig). Notice that the picture is symmetrical, you can get away with doing only 1/4 of the problem and then multiplying your result by four (I'd do the part in quadrant 1). You might need to make multiple pictures with different "a" vallaies to fully understand what the "a" variable is doing before tackling the next step. Your integral for quadrant 1 is going to start out looking like / ydw (remember, you chose your "a" to be a number in order to make your picture, 0 but the problem is asking for a result that could work for an arbitrary constant "a" value). In your work, make sure you clearly explain and justify WHY this integral is appropriate to represent the area of the shape in quadrant 1. Replace "y" with the given thing in the problem. Use the "x" in the problem and take derivative on both sides to find "dx". Adjust your bounds, and rewrite your integral in terms of theta. From here you should be able to complete the problem (your final answer will have an "a" in it somewhere)