Calculate the Second Diagonal in a Deltoid with Area 18 cm² and First Diagonal 3 cm

Shown below is the deltoid ABCD.

The diagonal AC is 3 cm long.

The area of the deltoid is 18 cm².

Calculate the diagonal DB.

Video Solution

Solution Steps

00:00 Calculate diagonal DB

00:03 We'll use the formula for calculating rhombus area

00:09 (diagonal times diagonal) divided by 2

00:19 We'll substitute appropriate values according to the data and solve for DB

00:29 Multiply by 2 to eliminate the fraction

00:38 Isolate DB

00:50 And this is the solution to the question

Step-by-Step Solution

The goal here is to find the diagonal $DB$ of the deltoid. Given:

We utilize the formula relating the diagonals and area of a deltoid:

\text{Area} = \frac{1}{2} \times d_1 \times d_2

Here, $d_1 = 3$ cm (given as diagonal $AC$ ) and the area is given as 18 cm $^2$ . We are solving for $d_2 = DB$ .

Substituting the known values into the formula:

18 = \frac{1}{2} \times 3 \times DB

First, multiply both sides by 2 to clear the fraction:

36 = 3 \times DB

Now, solve for $DB$ by dividing both sides by 3:

DB = \frac{36}{3} = 12 \, \text{cm}

Therefore, the diagonal $DB$ of the deltoid is $12 \, \text{cm}$ .