Answer:
Step-by-step explanation:
To calculate the total surface area, you first need to calculate the surface area of one of the 4 triangles and multiply that by 4.
We can solve this two ways (I would recommend using 2).
1)
Using herons formula:
a, b, c = different sides of the triangle (length)
s = (a + b + c) / 2
a = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
If we input values:
a = b = c = 6.5m
s = (3 * 6.5) / 2 = 9.75
[tex]\sqrt{s(s-6.5)^{3} }[/tex] which is about 18.29478 (exact answer: [tex]3.25\sqrt{31.6875}[/tex])
18.29478 * 4 = the entire area = 73.17912 m^2
exact whole area: [tex](13\sqrt{31.6875})m^{2}[/tex]
2)
Each of the four triangles can be divided into 2 more triangles.
(2 * 4 = 8 = total amount of new small triangles)
How we calculate the area of one of the new small ones:
(h * w) / 2 = a
h = 5.6m
w = (width of one of the four triangles width divided by 2) = 3.25m
3.25m * 5.6m = 18.2m^2
18.2m^2 / 2 = 9.1m^2
There are 8 of the new small triangles in the biggest triangle made up of four smaller ones.
So if we take 9.1m^2 * 8, we get the total area!
Total area: 72.8m^2
Happy to help you!
If you have any questions, ask in the comments below!
Have a good day! (●'◡'●)
