Calculate Diagonal Length X in a Deltoid with Area 20 cm²

Shown below is the deltoid ABCD.

The diagonal AC = X

Diagonal DB = 5

The area of the deltoid is 20 cm².

Calculate X.

Video Solution

Solution Steps

00:00 Calculate X

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

00:06 (diagonal times diagonal) divided by 2

00:10 We'll substitute appropriate values and solve for X

00:19 We'll multiply by 2 to eliminate the fraction

00:24 Isolate X

00:31 And this is the solution to the question

Step-by-Step Solution

To calculate $X$ , follow these steps:

Step 1: Use the area formula for a deltoid $\text{Area} = \frac{1}{2} \times d_1 \times d_2$ .
Step 2: Given the area $= 20 \, \text{cm}^2$ , $d_1 = X$ , and $d_2 = 5$ , substitute these into the formula.
Step 3: Set the equation: $20 = \frac{1}{2} \times X \times 5$ .
Step 4: Simplify and solve for $X$ .

Now, let's solve:

Start with the equation $20 = \frac{1}{2} \times X \times 5$ .

This simplifies to $20 = \frac{5X}{2}$ .

Multiply both sides by 2 to eliminate the fraction:

$40 = 5X$ .

Divide both sides by 5:

$X = \frac{40}{5}$ .

Simplifying gives us $X = 8$ .

Therefore, the length of diagonal $AC$ is $X = 8 \, \text{cm}$ .