Answer:
[tex]\large\boxed{A=480\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a kite:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonal
Look at the picture.
Use the Pythagorean theorem.
[tex]x^2+5^2=13^2[/tex]
[tex]x^2+25=169[/tex] subtract 25 from both sides
[tex]x^2=144\to x=\sqrt{144}\\\\x=12\ m[/tex]
Therefore d₁ = (2)(12 m) = 24 m.
[tex]y^2+12^2=37^2[/tex]
[tex]y^2+144=1369[/tex] subtract 144 from both sides
[tex]y^2=1225\to y=\sqrt{1225}\\\\y=35\ m[/tex]
Therefore d₂ = 5 + 35 = 40 m.
Substitute:
[tex]A=\dfrac{(24)(40)}{2}=(24)(20)=480\ m^2[/tex]
