Answer:
Third option is correct. The area of figure is 21.25m^2.
Step-by-step explanation:
The area of a kite is
[tex]A=\frac{1}{2}(d_1\times d_2)[/tex]
Both diagonals are perpendicular. Longer diagonal bisects the smaller diagonal.
In triangle ABO,
[tex]\tan45^{\circ}=\frac{BO}{AO}[/tex]
[tex]1=\frac{BO}{2.5}[/tex]
[tex]2.5=BO[/tex]
The length of BD is
[tex]BD=2\times BO=2\times 2.5=5[/tex]
The length of AC is
[tex]6+2.5=8.5[/tex]
The area of kite ABCD is
[tex]A=\frac{1}{2}(AC\times BD)[/tex]
[tex]A=\frac{1}{2}(8.5\times 5)[/tex]
[tex]A=21.25[/tex]
Therefore third option is correct. The area of figure is 21.25m^2.
