Question

QUESTION 2 The "Snap From" feature asks you to first and then QUESTION 3 An enclosed space is defined by 5 points whose coordinates in the world coordinate system are: 0,0 -1.82,3.47 5.63,2.21 3.75,-2.34 2.19,1.68 (and ends back at 0,0) There is a circle who's center is at the second point (-1.82,3.47) whose radius is 1.875. The space that is to be used for the question (Space A) is the enclosed space minus the portion of the circle inside the enclosed space. The perimeter of Space A is , and the area of Space A is (give 4 decimal places)

Answer 1

we have find the area and perimeter of orange region

+ 15 10 F-183, 3477 (5.63, 2.21) (2.199 (3.75, 2.34) -10 -5 0 5 10 (0,0) -5 -10 -15 -20

angle of black region arc = $tan\theta = \left | \frac{m_{2}-m_{1}}{1-m_{2}*m_{1}} \right |$

$m_{1} = \frac{2.21-3.47}{5.63+1.83}$  

m1 = -0.168

similarly $m_{2} = \frac{0-3.47}{0+1.83}$

m2 = 1.896

$tan\theta = \left | \frac{m_{2}-m_{1}}{1-m_{2}*m_{1}} \right |$

$tan\theta =$1.49

$tan\theta =$$\theta = 56.14$

length of arc = radius*angle in radian = 1.875* 56.14*3.14/180 = 1.836

perimeter of orange region = perimeter of whole polygon - perimeter of black region

                                       = $\sqrt{(3.75-0)^{2}+(2.34-0)^{2}$ $+ \sqrt{(5.63-3.75)^{2}+(2.21-2.34)^{2}}$$+ \sqrt{(5.63+1.83)^{2}+(2.21-3.47)^{2}}$$+ \sqrt{(-1.83-2.19)^{2}+(3.47-1.6)^{2}}$$+ \sqrt{(2.19-0)^{2}+(1.6-0)^{2}}$ + 2 *1.875 + 1.836

= 4.420 + 1.883+ 7.56 + 4.43+ 2.71 + 2*1.875 +1.836

= 29.3012 is the required perimeter