An antique map was found in the attic of a local courthouse. It shows some measurementsfrom a local farm that was divided into 5 parts. Some of the measurements have faded withage, so you must find the remaining measurements, as well as calculate the total area andperimeter of the outside of the property. All lengths are measured in miles.

Answer:Perimeter: 26.2611 milesTotal area: 41 milesStep-by-step explanation:The map can be seen in the figure attached.From the Pythagorean Theorem: AC^2 = 3^2 + 4^2  AC = sqrt(25) AC = 5 From the Law of Cosines,  AD^2 = 3.1623^2 + 5^2 - 2*3.1623*5*cos(71.5651°) AD = sqrt(25) AD = 5 From the Law of Sines: 7.8102/sin(∠EDA) =  5/sin(38.8845°) 7.8102*sin(38.8845°)/5 = sin(∠EDA) arcsin(0.9805) = ∠EDA 101.3117° = ∠EDA (the obtuse solution) The addition of the 3 angles of a triangle must be equal to 180°, then:  ∠EAD = 180° - 38.8845° - 101.3117° = 39.8038° From the picture: ∠EFA + ∠GFA = 180° ∠GFA = 180° - 120.9638° ∠GFA = 59.0362° The addition of the 3 angles of a triangle must be equal to 180°, then:  ∠GFA + ∠FGA + ∠GAF = 180° ∠GAF = 180° - 59.0362° - 90° ∠GAF = 30.9638° From the picture: ∠FAE + ∠GAF + ∠EAD = 90° ∠FAE = 90° - 30.9638° - 39.8038° ∠FAE = 19.2324° From Law of Sines: ED/sin(39.8038°) = 5/sin(38.8845°) ED = 5*sin(39.8038°)/sin(38.8845°) ED = 5.0988 From Law of Sines: EF/sin(19.2324°) = 7.8102/sin(120.9638°)EF = 7.8102*sin(19.2324°)/sin(120.9638°)EF = 3From definition of Sine:sin(∠GAF) =  GF/5.831GF = sin(30.9638°)*5.831GF = 3From definition of Cosine:cos(∠GAF) =  GA/5.831GA = cos(30.9638°)*5.831GA = 5Perimeter = 3+4+3.1623+5.0988+3+3+5=26.2611 milesArea of the triangles:ΔABC = (1/2)*3*4 = 6 milesΔADC = (1/2)*5*3.1623*sin(71.5651°) =7.5 milesΔADE = (1/2)*7.8102*5.0988*sin(38.8845°) =  12.5 milesΔAEF = (1/2)*3*5.831*sin(120.9638°) = 7.5 milesΔAFG = (1/2)*5*3 = 7.5 milesTotal area = 6 + 7.5 + 12.5 + 7.5 + 7.5 = 41 miles