Land area calculation/verification

Question - What is the area in metres squared of lot 2 in the below image, Does the value of 30.64 as indicated next to the red arrow appear to be correct and in line with this?

I am trying to work out/verify the area of lot 2 in the below diagram. Not going to lie, I have spent a few hours over a few days on this already and haven't come up with the same land area as listed (4992m2). I tried a couple of online calculators as well with no luck. Hoping there is a kind soul that is willing to try and flex their mental abilities in return for gratitude.

I appreciate gratitude doesn't pay the bills but it's better than someone crop dusting you on their way off the bus. Kids, stay in school.

I have noted dimensions listed in red. Please note the additional 10m that needs to go on top of the 73.36 when looking at the height of lot 1.

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  • @ Diophantus: The heigh h can actually be computed using pythagorean theorem. Indeed h^2=(49.42)^2- (132.21-98.81)^2=1326.7764, and hence h= 36.4249. So the number indicated in red is 36.42. Using this value for h, the area of lot 2 is [(132.21+98.81)/2 ]*36.42=4206.87 m^2. However, if we take into account an additional 10m in the sides, i.e. consider the length of the sides to be 132.21+10 and +98.81+10, then the computed area seems to be close to 4992, which is what in indicated.

  • @ Diophantus: Please add more details as an attachment, if necessary, to help March_of_the_inane understand the above argument

  • @diophantus Unwanted to confirm the above includes the 4.05 by 114.01 area (E3). I am wanting to pop the calculation into an email to the agent to clarify. I am locked down currently or I would go measure the block myself. If a succient paragraph summary of it could be given that would be great.

  • * I wanted

  • @ Diophantus: The sides of the lot are indeed : 132.21+4 and 98.81+4+4.05. Please compute h as above and revise your solution and and upload it as an attachment.

  • I think the 132.21 is representative of the lot2, the 4 that you note is lot 3. Similar to the 98.81+4.05, the 4 would be for lot 3. Though if including those numbers gives us the 4992, we know how they calculated that figure. It is more than enough land to be honest, my main concern here is h/the value they stated as 30.64 as it will impact orientation of a house.

  • Its a 6 sided shape. I dont think my answer was addressed, but I will find someone else that can help. I highlighted the areas involved in yellow, the solid lines indicate the block.

  • @ March_of_the_inane: You should not accept any answer unless you are 100% happy with the solution.

  • @ Diophantus: Please do not accept to answer questions unless you feel that you have the time and expertises to clear all the doubts of the answerer.

  • March_of_the_inane: We asked a member of our scientific team to write a solution which is attached. Let us know if you need any clarifications. If you want to see more sophisticated calculations leading to the exact land size, you may post another question. Make sure to be very clear about what you are asking to be done.

  • 39.98 https://www.reddit.com/r/askmath/comments/pb61ih/area_of_an_irregular_shape_land_plot/?utm_medium=android_app&utm_source=share

The answer is accepted.