Answer:
63.966
Step-by-step explanation:
Area of a kite is
![\frac{pq}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bpq%7D%7B2%7D%20)
where p and q are the diagonals.
The horinzontial diagonal is 8.
We need to find the vertical diagonal length.
The top triangle diagonal measure is
![{4}^{2} + {x}^{2} = {7}^{2}](https://tex.z-dn.net/?f=%20%7B4%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20%7B7%7D%5E%7B2%7D%20)
![16 + {x}^{2} = 49](https://tex.z-dn.net/?f=16%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%2049)
![{x}^{2} = 33](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%2033)
![x = \sqrt{33}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B33%7D%20)
The bottom triangle diagonal measure is
![{4}^{2} + {x}^{2} = {11}^{2}](https://tex.z-dn.net/?f=%20%7B4%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20%7B11%7D%5E%7B2%7D%20)
![1 6 + {x}^{2} = 121](https://tex.z-dn.net/?f=1%206%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%20121)
![{x}^{2} = 105](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20105)
![x = \sqrt{105}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B105%7D%20)
Add the two diagonals.
![\sqrt{105} + \sqrt{33}](https://tex.z-dn.net/?f=%20%5Csqrt%7B105%7D%20%20%2B%20%20%5Csqrt%7B33%7D%20)
Substitute this in for the formula
![\frac{8 \times ( \sqrt{105} + \sqrt{33} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%20%5Ctimes%20%28%20%5Csqrt%7B105%7D%20%20%2B%20%5Csqrt%7B33%7D%20%20%7D%7B2%7D%20)
Which simplified gu
Ives us
![63.966](https://tex.z-dn.net/?f=63.966)
Round if neededd.