Deltoid Area Problem: Calculate Side AC Given Area 32cm² and Diagonal DB=4

Question

Given the deltoid ABCD

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

00:00 Calculate AC

00:03 We'll use the formula for calculating the area of a kite

00:07 (diagonal times diagonal) divided by 2

00:18 We'll substitute appropriate values according to the given data and find AC

00:22 We'll multiply by 2 to eliminate the fraction

00:31 We'll isolate AC

00:37 And this is the solution to the question

To solve for $AC$ in the deltoid, use the area formula:

Step 1: The area of a deltoid is given by $A = \frac{1}{2} \times p \times q$ , where $p$ and $q$ are diagonals.
Step 2: For this problem, set $p = DB = 4$ cm, and $q = AC$ (unknown).
Step 3: Substitute the values: $32 = \frac{1}{2} \times 4 \times AC$ .

Now, solve for $AC$ :
$32 = \frac{1}{2} \times 4 \times AC$
$32 = 2 \times AC$
Divide both sides by 2:
$AC = \frac{32}{2} = 16 \, \text{cm}$

The side $AC$ is therefore 16 cm.

16 cm