Finding Side Length AC in a Deltoid with Area 72 cm² and MD = 3 cm

Given below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 72 cm².

What is the length of the side AC?

Video Solution

Solution Steps

00:12 Let's find A C, the diagonal of the kite.

00:16 In a kite, the main diagonal crosses the secondary diagonal at a right angle.

00:29 Remember, each side is the sum of its segments.

00:34 We'll use the formula for the area of a kite.

00:38 Multiply both diagonals, then divide by 2.

00:44 Substitute the given values to find A C.

00:53 First, divide 6 by 2.

00:57 Next, isolate A C to solve.

01:06 And that's how we solve this problem!

Step-by-Step Solution

To solve for the length of $AC$ in the deltoid:

Given $MD = 3$ cm, which implies $BD = 2 \times MD = 6$ cm.
The area of the deltoid is given by the formula: $\text{Area} = \frac{1}{2} \times AC \times BD$ .

Putting the known values into the formula:
$72 = \frac{1}{2} \times AC \times 6$ .

To isolate $AC$ , multiply both sides by 2:

$144 = AC \times 6$ .

Divide both sides by 6 to solve for $AC$ :

$AC = \frac{144}{6} = 24 \, \text{cm}$ .

Therefore, the length of the side $AC$ is $24 \, \text{cm}$ .