Deltoid Geometry: Finding AC Length Given Area 60 cm² and BD = 12 cm

Question

Given the deltoid ABCD

Side length BD equals 12 cm

The area of the deltoid is equal to 60 cm².

Find the length of the side AC

00:00 Find AC

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

00:07 (diagonal times diagonal) divided by 2

00:12 We'll substitute appropriate values according to the given data and solve for AC

00:21 Divide 12 by 2

00:25 Isolate AC

00:34 And this is the solution to the question

To find the length of side $AC$ in the given deltoid:

Step 1: Write down the area formula for a kite: $S = \frac{1}{2} \times BD \times AC$ , where $S$ is the area, and $BD$ and $AC$ are the diagonals.
Step 2: Plug in the known values: $60 = \frac{1}{2} \times 12 \times AC$ .
Step 3: Simplify the equation: $60 = 6 \times AC$ .
Step 4: Solve for $AC$ :

$AC = \frac{60}{6} = 10$ cm.

Therefore, the length of side $AC$ is $10$ cm.

$10$ cm