Calculate the Area of Deltoid ABCD with Diagonals 8 and 9

To solve this problem, we'll calculate the area of the deltoid $ABCD$ using the formula for the area of a kite or deltoid, which depends on its diagonals.

• Step 1: Identify the given information
  The given diagonals are $AC = 9$ cm and $BD = 8$ cm.

• Step 2: Apply the area formula for a deltoid
  The area $A$ of a deltoid with perpendicular diagonals is given by:

• $A = \frac{1}{2} \times d_1 \times d_2$

• Step 3: Perform the calculation
  Substitute the given diagonal lengths into the formula:
  $A = \frac{1}{2} \times 9 \times 8$
  $A = \frac{1}{2} \times 72$
  $A = 36$

Thus, the area of the deltoid $ABCD$ is $36$ cm².