Answer:
30.51 units^2
Step-by-step explanation:
Well to find the area of a triangle without height we use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
To find S we use the following formula,
[tex]S = \frac{1}{2} (a+b+c)[/tex]
So a b and c are the sides of a triangle, we'll start with the left triangle.
S = 1/2(7 + 5.22 + 7.4)
S = 1/2(19.62)
S = 9.81
Now we can plug in 9.81 for S,
[tex]A = \sqrt{9.81(9.81-a)(9.81-b)(9.81-c)}[/tex]
[tex]A = \sqrt{9.81(9.81-7)(9.81-5.22)(9.81-7.4)}[/tex]
[tex]A = \sqrt{9.81(2.81)(4.59)(2.41)}[/tex]
[tex]A = \sqrt{9.81(31.083939)}[/tex]
[tex]A = \sqrt{304.93344159}[/tex]
[tex]A = 17.46234353086664[/tex]
But we can just simplify that to the nearest hundredth place which is,
17.46.
Now for the next triangle,
[tex]S = \frac{1}{2} (6.36 + 6.85 + 7.4)[/tex]
[tex]S = \frac{1}{2} (20.61)[/tex]
[tex]S = 10.305[/tex]
Plug in 10.305 for S,
[tex]A = \sqrt{10.305(10.305-6.36)(10.305-6.85)(10.305-7.4)}[/tex]
[tex]A = \sqrt{10.305(3.945)(3.455)(2.905)}[/tex]
[tex]A = \sqrt{10.305(16.534975)}[/tex]
[tex]A = \sqrt{170.392917375}[/tex]
A = 13.053463807549
We can round it to the nearest hundredth,
A = 13.05
So we just add 17.46 + 13.05
= 30.51 units^2
Thus,
the area of the figure is 30.51 units^2.
Hope this helps :)
