Calculate Triangle Fit in Deltoid: 8cm and 14cm Dimensions Problem

To solve this problem, we'll calculate the areas to determine how many times $\triangle ABC$ fits into $ABCD$:

• Step 1: Calculate the area of the deltoid $ABCD$ using the formula:
  $\text{Area of deltoid} = \frac{1}{2} \times AC \times DB = \frac{1}{2} \times 8 \times 14 = 56 \, \text{square cm}$

• Step 2: Calculate the area of $\triangle ABC$:
  $\triangle ABC$ has diagonal $AC = 8 \, \text{cm}$, so $\text{Area of} \, \triangle ABC = \frac{1}{2} \times AC \times DB = \frac{1}{2} \times 8 \times \frac{14}{2} = 28 \, \text{square cm}$

• Step 3: Determine how many times $\triangle ABC$ fits into deltoid $ABCD$:
  Since the area of the deltoid is $56 \, \text{square cm}$ and the area of $\triangle ABC$ is $28 \, \text{square cm}$, then:
  $\frac{\text{Area of deltoid}}{\text{Area of} \, \triangle ABC} = \frac{56}{28} = 2$

Therefore, triangle $\triangle ABC$ fits $\textbf{2}$ times into the deltoid $ABCD$.