Question

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

Answer 1

I'll label the triangles as triangles 1, 2, 3, 4, and 5

starting with triangle 5, this is a 3-4-5 right triangle, so label AC as 5

now with triangle 4, you have two sides and the angle in between, which is the perfect setup for law of cosines to find length AD

moving to triangle 3, use law of cosines again, with angle E as the reference, to find ED

for triangle 2, you have 2 sides and an angle, so you can find the missing side EF

assuming EG is a straight line, you have a linear angle pair (<EFA and <AFG) so you can find <AFG

Answer 2

now, you have to do a bit of back-tracking to get more info about triangle 1

you should have all the side lengths for triangles 2 and 3. you can find the angles <EAF and <DAE. now, using the fact that <EAF and <DAE and <GAF add up to 90 degrees, find <GAF.

use law of sines to find FG and GA. that should be all the outside side lengths, so you can simply add them up to find perimeter. for area, I believe you can use Heron's formula.