Answer:
19.3 square units .
Step-by-step explanation:
∠D=∠F=52°
Opposite sides of equal angles are equal .
So, DE=EF =6.3
Now sum of all angles of triangle is 180°
So, ∠D+∠F+∠E = 180°
52°+52°+∠E =180°
104°+∠E =180°
∠E =180°-104°
∠E =76°
Now to find the length of DF we will use law of cosines
[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]
[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]
[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]
[tex]DF^2=79.38+79.38 (0.2419)[/tex]
[tex]DF^2=98.582[/tex]
[tex]DF=\sqrt{98.582}[/tex]
[tex]DF=9.9[/tex]
Now we are supposed to find the area of triangle
To calculate the area of given triangle we will use the heron's formula :
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
a,b,c are the side lengths of triangle
Now substitute the values :
[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]
[tex]s =11.25[/tex]
[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]
[tex]Area = 19.2907[/tex]
Hence the area of the triangle is 19.2907 ≈19.3 square units .
