Deltoid Diagonal Calculation: Finding AC When Area = 24cm² and DB = 4

Look at the deltoid ABCD below.

Diagonal DB = 4

The area of the deltoid is 24 cm².

Calculate the diagonal AC.

Video Solution

Solution Steps

00:00 Calculate diagonal AC

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

00:06 (diagonal times diagonal) divided by 2

00:15 We'll substitute appropriate values according to the given data and solve for AC

00:26 Divide 4 by 2

00:31 Isolate AC

00:39 And this is the solution to the problem

Step-by-Step Solution

To find the length of diagonal AC of the deltoid, follow these steps:

We know the formula for the area of a deltoid (kite) given by $S = \frac{1}{2} \times d_1 \times d_2$ . Here, $S = 24 \, \text{cm}^2$ , $d_1 = AC$ , and $d_2 = BD = 4 \, \text{cm}$ .
Substitute the known values into the formula: $24 = \frac{1}{2} \times AC \times 4$ .
Simplify the equation: $24 = 2 \times AC$ because $\frac{1}{2} \times 4 = 2$ .
Solve for $AC$ by dividing both sides by 2: $AC = \frac{24}{2}$ .
This simplifies to $AC = 12$

Therefore, the length of diagonal AC is $12 \, \text{cm}$ .