Explanation for Question 29 From the Math (Calc) Section on the 2020 October Sat
So question nine asks or 29 asked us to find the area of a 2 rather obscure part of the circle, 3 right? The shaded area right here. 4 And so there's no one equation that can give you that area. 5 But what we can do is take the area of the sector, 6 which is the area around this whole thing here, 7 the whole entire piece of the pie, and then subtract the area of the 8 equal lateral equal lateral triangle. 9 That's within it. Now we know that this triangle is equal lateral because we 10 have two sides that are four and an angle that are 60. 11 So that means that all of our angles are going to be 60, 12 which makes it equal lateral. Right? And so the first thing we can do 13 is find the area of that sector, which is given by this equation here, 14 where it's like, you're taking a percentage of the area of the whole circle. 15 And so our area or our angle measure is 60 degrees, 16 right? So we do 60 over 360, 17 probably a good idea to simplify that right off the bat. 18 And so that can give us one over six and 19 multiply that by PI times 16, 20 the radius squared. Now we can even further simplify that because, 21 um, two goes into both six and 16, 22 so this becomes eight over three, right? 23 And so the area of our sector is going to be eight PI over 24 three. Now we can find the area of that equal lateral triangle. 25 And this is the special equation for area of an equal lateral triangle. 26 It's really useful for equal lateral triangles, 27 but it doesn't work for any other...