Deltoid Area Calculation: Finding Area with Height 13 and Base 17.5

To find the area of the deltoid, we will use the formula for the area of a kite which is based on the lengths of its diagonals:

$\text{Area} = \frac{d_1 \times d_2}{2}$

Given:

• $d_1 = AC = 13$ cm, and
• $d_2 = BD = 17.5$ cm.

Now, substitute these values into the formula:

$\text{Area} = \frac{13 \times 17.5}{2}$

Calculating inside the parentheses:

$13 \times 17.5 = 227.5$

Therefore, the area is:

$\text{Area} = \frac{227.5}{2} = 113.75$ cm²

The area of the deltoid ABCD is $113.75$ cm².

The correct answer choice is: $113.75$ cm².