Calculate Area Ratio: Deltoid ABCD in Triangle ABD with AC=4cm, DB=6cm

To solve this problem, follow these steps:

• Step 1: Calculate the area of deltoid ABCD using the diagonals AC and DB.
• Step 2: Determine how many times the area of deltoid ABCD fits into the area of triangle ABD.

Now, let's work through each step:

Step 1: Since deltoid ABCD is a kite, its area is given by: $\text{Area}_{\text{deltoid}} = \frac{1}{2} \times \text{AC} \times \text{DB} = \frac{1}{2} \times 4 \times 6 = 12 \, \text{cm}^2.$

Step 2: We divide the area of triangle ABD by the area of deltoid ABCD to find how many times it fits: $\text{Number of times} = \frac{\text{Area}_{\text{triangle}}}{\text{Area}_{\text{deltoid}}} = \frac{36 \, \text{cm}^2}{12 \, \text{cm}^2} = 3.$

Therefore, the deltoid ABCD can fit 3 times inside triangle ABD.

Thus, the answer is $3$.