Answer:
63.966
Explanation:
Area of a kite is
![(pq)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/u69yqpjpz8majmz25f4zex2hi9fduto14m.png)
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://img.qammunity.org/2022/formulas/mathematics/high-school/28gcze5vxst2of3ety3v5kedk7lfk4zoix.png)
![16 + {x}^(2) = 49](https://img.qammunity.org/2022/formulas/mathematics/high-school/xi4iev19z0b3skeuywa5urp8om0enspgtt.png)
![{x}^(2) = 33](https://img.qammunity.org/2022/formulas/mathematics/high-school/txrdrv7opwb93m1x1a8phsn7aa8v1mqcrk.png)
![x = √(33)](https://img.qammunity.org/2022/formulas/mathematics/college/gua4qmdchh4w651yooqmi5uwvyfcucp25z.png)
The bottom triangle diagonal measure is
![{4}^(2) + {x}^(2) = {11}^(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/wcw8npn4vp27lxb3fz19lsz65jisyizola.png)
![1 6 + {x}^(2) = 121](https://img.qammunity.org/2022/formulas/mathematics/high-school/zy4o8ov1saqmyjr99nckyt5azgmoebjsa6.png)
![{x}^(2) = 105](https://img.qammunity.org/2022/formulas/mathematics/high-school/yv2mo0e01e9r401dfdchrlnsdzugtaf7jj.png)
![x = √(105)](https://img.qammunity.org/2022/formulas/mathematics/high-school/r3e4gsqd6gi8nwwjatvmjh2ci3z7w90mnr.png)
Add the two diagonals.
![√(105) + √(33)](https://img.qammunity.org/2022/formulas/mathematics/high-school/3lr2quoffaan15h57xtj3zoaxuxcnsa2pc.png)
Substitute this in for the formula
![(8 * ( √(105) + √(33) )/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ffkctlqkrs6w69ci2bj9kawnieffwq3avo.png)
Which simplified gu
Ives us
![63.966](https://img.qammunity.org/2022/formulas/mathematics/high-school/enlwm4octbykvvwi8oibntf4fl9cwypx3m.png)
Round if neededd.