Final answer:
The area of a kite is found by multiplying the lengths of its diagonals and dividing by two. Given AE, CE, and BE, we find the full length of the second diagonal (12 cm) and calculate the area as 108 cm², a result not listed among the provided options.
Step-by-step explanation:
The question asks us to calculate the area of a kite given the lengths of its diagonals AE, CE, and BE. To find the area of a kite, we need the lengths of its diagonals. However, in the given problem, only one full diagonal (CE) and one-half diagonal (BE) are provided because the other half diagonal (AE) is for the other diagonal's length.
In a kite, the diagonals are perpendicular bisectors of each other. Therefore, we can calculate the full length of the other diagonal by doubling AE, which is 6 cm. So the full length of the second diagonal will be AE + AE = 6 cm + 6 cm = 12 cm.
To find the area of the kite, we multiply the lengths of the diagonals and then take half of that product:
- Let AB represent the full length of the second diagonal, then AB = 12 cm.
- Now, multiply the lengths of the diagonals AB and CE, which gives us 12 cm * 18 cm = 216 cm².
- Finally, take half of this product to get the area of the kite: (1/2) * 216 cm² = 108 cm².
Therefore, the area of the kite is 108 cm², which is not one of the options given in the multiple-choice answers above, indicating a possible mistake in the question or the provided answer choices.