Answer:
Ok so what you have to do to is basically apply Pythagoras Theorem
Step-by-step explanation:
The hypotenuse squared is equal to the sum of the squares of the legs of a right-angle triangle.
[tex]c^2 = a^2 + b ^2[/tex]
Assuming:
c = 10 [tex]\rightarrow[/tex] hypotenuse
a = 6.84 [tex]\rightarrow[/tex] adjacent leg (base of the triangle)
b = ? [tex]\rightarrow[/tex] opposite leg (height of triangle)
[tex]10^2 = 6.84^2 + b^2[/tex]
[tex]b^2 = 10^2 - 6.84^2[/tex]
[tex]b = \sqrt{(10)^2-(6.84)^2}[/tex]
[tex]b = 7.295[/tex]
With that, you can calculate the area of the triangle:
[tex]A_{triangle} = \frac{a*b}{2}[/tex]
[tex]A_{triangle} = \frac{6.84*7.295}{2}[/tex]
[tex]A_{triangle} = 24.95[/tex]
And as your polygon has 9 sides, you can assume that you have 9 of this triangles, so the total area would be:
[tex]A = 9*24.95[/tex]
[tex]A = 224.55[/tex]
And rounding this result to the nearest hundreth:
[tex]A = 220[/tex]
