Calculate the Area of a Deltoid: Given Height 5 and Base 22

Q: What's the difference between a kite and a deltoid?

A deltoid is just another name for a kite! Both are quadrilaterals with two pairs of adjacent sides that are equal in length.

Q: How do I identify the diagonals in the diagram?

The diagonals are the lines that connect opposite vertices. In this problem, one diagonal is vertical (length 5) and the other is horizontal (length 22).

Q: Why do we multiply by 1/2 in the formula?

The diagonals of a kite divide it into 4 right triangles. The formula $ \frac{1}{2} \times d_1 \times d_2 $ calculates the total area of all 4 triangles combined.

Q: Do the diagonals have to be perpendicular?

Yes! In a kite, the diagonals are always perpendicular (meet at 90°). This is why the area formula works - it's based on perpendicular diagonal intersection.

Q: What if I mixed up which measurement is which diagonal?

No problem! Since we're multiplying the diagonals, the order doesn't matter. $ 22 \times 5 = 5 \times 22 = 110 $, so you'll get the same answer either way.

Kite 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'll use the formula to calculate the kite's area

00:08 (diagonal times diagonal) divided by 2

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

00:24 Divide 22 by 2

00:32 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 solve the problem of finding the area of the deltoid $ABCD$ , we will use the area formula for a kite. The formula is:

$\text{Area} = \frac{1}{2} \times d_1 \times d_2$

Given:

$d_1 = 22$ cm (one diagonal of the deltoid)
$d_2 = 5$ cm (the other diagonal of the deltoid)

Substitute the given values into the formula:

$\text{Area} = \frac{1}{2} \times 22 \times 5$

$\text{Area} = \frac{1}{2} \times 110$

$\text{Area} = 55 \text{ cm}^2$

Therefore, the area of the deltoid $ABCD$ is $\boxed{55}$ square centimeters.

Final Answer

$55$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area of kite equals half the product of diagonals
Technique: $\text{Area} = \frac{1}{2} \times 22 \times 5 = 55$
Check: Verify diagonals are perpendicular and bisect each other ✓

Common Mistakes

Avoid these frequent errors

Using side lengths instead of diagonals
Don't use the side lengths of the kite in the area formula = completely wrong answer! The kite area formula specifically requires the diagonal lengths, not the side measurements. Always identify which measurements are diagonals first.

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's the difference between a kite and a deltoid?

A deltoid is just another name for a kite! Both are quadrilaterals with two pairs of adjacent sides that are equal in length.

How do I identify the diagonals in the diagram?

The diagonals are the lines that connect opposite vertices. In this problem, one diagonal is vertical (length 5) and the other is horizontal (length 22).

Why do we multiply by 1/2 in the formula?

The diagonals of a kite divide it into 4 right triangles. The formula $\frac{1}{2} \times d_1 \times d_2$ calculates the total area of all 4 triangles combined.

Do the diagonals have to be perpendicular?

Yes! In a kite, the diagonals are always perpendicular (meet at 90°). This is why the area formula works - it's based on perpendicular diagonal intersection.

What if I mixed up which measurement is which diagonal?

No problem! Since we're multiplying the diagonals, the order doesn't matter. $22 \times 5 = 5 \times 22 = 110$ , so you'll get the same answer either way.

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