Deltoid Practice Problems: Kite Properties & Solutions

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 $\frac{8\cdot DB}{2}=32$

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

To determine if we can calculate the area of the kite, let's consider the steps we would use given complete data:
To calculate the area of a kite, we typically use the formula:

where $d_1$ and $d_2$ represent the lengths of the kite's diagonals.

In this case:

• We are given that diagonal $DB = d_1 = 10$ cm.
• However, we lack the length of the other diagonal, $AC = d_2$.

Without knowing $AC$, we cannot apply the formula to calculate the area. Thus, given the information provided, it is not possible to determine the area of the kite.

Therefore, the solution to the problem is: It is not possible.

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

To find the area of a deltoid (also known as a kite), we need to make use of the given dimensions: the kite's longer diagonal ($AC$) and the shorter diagonal ($BD$). Here are the steps we'll follow:

• Step 1: Identify the key information.
• Step 2: Use the formula for the area of a kite.
• Step 3: Perform the calculation.

Let's go through each step in detail:

Step 1: Identify the key information
In the problem, the deltoid (kite) is described with vertices $A$, $B$, $C$, and $D$. From the diagram, we have the following measurements:

• The diagonal $AC = 19$ cm.
• The diagonal $BD = 5$ cm.

Step 2: Use the formula for the area of a kite
The area of a kite can be calculated using the formula: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.

Step 3: Perform the calculation
Now we substitute the given measurements into the formula:

$\text{Area} = \frac{1}{2} \times 19 \times 5$

Carrying out the multiplication:

$\text{Area} = \frac{1}{2} \times 95 = 47.5$

Thus, the area of the deltoid (kite) is $47.5$ cm².

This matches choice $\mathbf{3}$.