Calculate Deltoid Area: Given 10cm Diagonal and 40% Length Relationship

To solve the problem, we need to find the lengths of the diagonals and then calculate the area of the deltoid using these lengths.

• First, find the length of diagonal $AC$.

Given that $AC$ is 40% longer than $DB$, which is 10 cm:

$AC = 10 + 0.4 \times 10 = 10 + 4 = 14 \, \text{cm}$

• Now, apply the formula for the area of the deltoid:

The area $A$ of a deltoid can be calculated using the formula:

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

Substituting the given values ($d_1 = DB = 10 \, \text{cm}$ and $d_2 = AC = 14 \, \text{cm}$):

$A = \frac{1}{2} \times 10 \times 14 = \frac{1}{2} \times 140 = 70 \, \text{cm}^2$

Therefore, the area of the deltoid ABCD is 70 cm², which matches the given correct answer.