Deltoid Geometry: Find Variable b When Area = 144 cm²

ABCD is a deltoid.

Side BM equals 4 cm.

The area of the deltoid is equal to 144 cm².

Calculate b.

Video Solution

Solution Steps

00:00 Find B

00:03 In a kite, the main diagonal intersects the secondary diagonal

00:07 The whole side equals the sum of its parts

00:13 Here too, the whole side equals the sum of its parts

00:17 We'll use the formula for calculating the area of a kite

00:22 (diagonal times diagonal) divided by 2

00:27 We'll substitute appropriate values according to the given data and solve for B

00:37 Divide 8 by 2

00:44 Isolate B

00:53 And this is the solution to the question

Step-by-Step Solution

To solve the problem, we'll follow the steps outlined:

Let's break it down:

Step 1: We know the length of diagonal $BM = 4$ cm and the area of the deltoid is $144$ cm².

Step 2: The area of a deltoid is given by the formula:

$\text{Area} = \frac{1}{2} \times \text{Diagonal}_1 \times \text{Diagonal}_2$

Here, the diagonals correspond to line segments of the form $2b$ and $4b$ as represented in the setup of the problem.

Step 3: Substituting the values into the area formula, we have:

$\frac{1}{2} \times (2b) \times (4b) = 144$

Simplifying this, we get:

$4b^2 = 144 \quad \Rightarrow \quad b^2 = \frac{144}{4} = 36$

Therefore, solving for $b$ , we find:

$b = \sqrt{36} = 6$

Thus, the value of $b$ is $6$ .