Calculate the Area of Deltoid ABCD with Height 5 and Base 9

To solve the problem of finding the area of the deltoid ABCD, we can apply the following method:

• Step 1: Identify the diagonals:
  From the problem, $AC = 5$ cm and $BD = 9$ cm are the lengths of the diagonals.
• Step 2: Apply the area of deltoid formula:
  When diagonals intersect perpendicularly in a kite or deltoid shape, the area $A$ is given by:
  $A = \frac{1}{2} \times d_1 \times d_2$
  where $d_1 = 5$ cm and $d_2 = 9$ cm are the diagonals.
• Step 3: Substitute and calculate:
  $A = \frac{1}{2} \times 5 \times 9$
  $A = \frac{1}{2} \times 45$
  $A = 22.5$ cm²

Therefore, the area of the deltoid ABCD is $22.5$ cm².