Calculate Deltoid Area: Given 10cm Diagonal and 40% Length Relationship

Below is the deltoid ABCD.

Given in cm: DB = 10

Diagonal AC is 40% longer than diagonal DB.

Calculate the area of the deltoid.

Video Solution

Solution Steps

00:12 Let's find the area of the kite.

00:15 To do this, we'll use the formula for area of a kite.

00:19 It's diagonal one times diagonal two, divided by 2.

00:24 From the given data, let's find the ratio of the diagonals.

00:35 We will substitute the value of diagonal BD, given in the data, and then solve for diagonal AC.

00:43 First, we'll change the percentages into fractions to make it easier.

00:51 This gives us the length of diagonal AC.

00:59 Now, let's use these values in the area formula and solve it step by step.

01:11 And that's how we find the area of the kite!

Step-by-Step Solution

To solve the problem, we need to find the lengths of the diagonals and then calculate the area of the deltoid using these lengths.

Given that $AC$ is 40% longer than $DB$ , which is 10 cm:

$AC = 10 + 0.4 \times 10 = 10 + 4 = 14 \, \text{cm}$

The area $A$ of a deltoid can be calculated using the formula:

$A = \frac{1}{2} \times d_1 \times d_2$

Substituting the given values ( $d_1 = DB = 10 \, \text{cm}$ and $d_2 = AC = 14 \, \text{cm}$ ):

$A = \frac{1}{2} \times 10 \times 14 = \frac{1}{2} \times 140 = 70 \, \text{cm}^2$

Therefore, the area of the deltoid ABCD is 70 cm², which matches the given correct answer.