Deltoid Geometry: Finding AC Length Given Area 54 cm² and BD = 6 cm

Given the deltoid ABCD

Side length BD equals 6 cm

The area of the deltoid is equal to 54 cm².

Find the length of the side AC

Video Solution

Solution Steps

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

00:11 We'll substitute appropriate values according to the given data and solve for AC

00:23 Divide 6 by 2

00:30 Isolate AC

00:42 And this is the solution to the question

Step-by-Step Solution

To find the length of side $AC$ , follow these steps:

Step 1: Use the formula for the area of a deltoid: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$ .
Step 2: Set the known values into the equation, where $d_1 = BD = 6$ cm and the area is 54 cm $^2$ .
Step 3: Rearrange the formula to solve for $d_2$ (which is $AC$ ): $54 = \frac{1}{2} \times 6 \times AC$ .
Step 4: Simplify and solve for $AC$ : $54 = 3 \times AC$ .
Step 5: Divide both sides by 3 to isolate $AC$ : $AC = \frac{54}{3} = 18$ cm.

Therefore, the length of $AC$ is $18$ cm.