Calculate the Area of a Deltoid: Using 4 and 6 Unit Diagonals

Q: What exactly is a deltoid?

A deltoid (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Its diagonals are perpendicular, which is why we can use this simple area formula!

Q: Why do we divide by 2 in the formula?

The diagonals divide the deltoid into four right triangles. Multiplying the diagonals gives the area of a rectangle, but our shape is only half that area, so we divide by 2.

Q: Do the diagonal measurements include units?

Yes! In this problem, both diagonals are measured in centimeters, so our final answer is in square centimeters (cm²). Always check units in your final answer.

Q: How can I remember this formula?

Think of it like finding the area of a rectangle formed by the diagonals, then taking half of that area. Rectangle area = length × width, deltoid area = $ \frac{1}{2} $ × diagonal₁ × diagonal₂!

Deltoid Area with Diagonal Measurements

Given the deltoid ABCD

Find the area

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the kite

00:03 We will use the formula to calculate the area of a kite

00:07 (diagonal times diagonal) divided by 2

00:13 We'll substitute the appropriate values according to the given data and solve for the area

00:26 We'll divide 4 by 2

00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the deltoid ABCD

Find the area

Step-by-step solution

To find the area of deltoid $ABCD$ , we will use the known formula for the area of a deltoid based on its diagonals. Let's perform the calculation step-by-step:

Step 1: Identify the diagonals
From the problem, the diagonals are given as 4 cm and 6 cm.
Step 2: Apply the area formula
The area of a deltoid is calculated using the formula: $A = \frac{1}{2} \times d_1 \times d_2$
Step 3: Calculate the area
Substitute the diagonal lengths into the formula: $A = \frac{1}{2} \times 4 \times 6$
$A = \frac{1}{2} \times 24 = 12$ cm²

Thus, the area of deltoid $ABCD$ is $\mathbf{12}$ cm².

Final Answer

$12$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Deltoid area equals half the product of diagonal lengths
Technique: Apply $A = \frac{1}{2} \times 4 \times 6 = 12$ cm²
Check: Verify diagonals are perpendicular and formula gives $\frac{24}{2} = 12$ ✓

Common Mistakes

Avoid these frequent errors

Adding diagonals instead of multiplying
Don't add the diagonals like 4 + 6 = 10 and divide by 2 = 5 cm²! This ignores the area formula completely and gives a wrong result. Always multiply the diagonals first, then divide by 2.

Practice Quiz

Test your knowledge with interactive questions

Indicate the correct answer

The next quadrilateral is:

FAQ

Everything you need to know about this question

What exactly is a deltoid?

A deltoid (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Its diagonals are perpendicular, which is why we can use this simple area formula!

Why do we divide by 2 in the formula?

The diagonals divide the deltoid into four right triangles. Multiplying the diagonals gives the area of a rectangle, but our shape is only half that area, so we divide by 2.

Do the diagonal measurements include units?

Yes! In this problem, both diagonals are measured in centimeters, so our final answer is in square centimeters (cm²). Always check units in your final answer.

What if the diagonals were different lengths?

The formula stays the same! Whether diagonals are 3 and 8, or 5 and 10, you still use $A = \frac{1}{2} \times d_1 \times d_2$ . The deltoid doesn't need to be symmetric.

How can I remember this formula?

Think of it like finding the area of a rectangle formed by the diagonals, then taking half of that area. Rectangle area = length × width, deltoid area = $\frac{1}{2}$ × diagonal₁ × diagonal₂!

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