Deltoid Area Calculation: Finding Area with Height 13 and Base 17.5

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

A deltoid is just another name for a kite! Both are quadrilaterals with two pairs of adjacent sides that are equal and diagonals that meet at right angles.

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

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

Q: How do I identify which measurements are the diagonals?

Diagonals connect opposite vertices (corners) and cross inside the shape. In this problem, diagonal AC = 13 and diagonal BD = 17.5, both shown as colored lines in the diagram.

Q: What if the diagonals aren't perpendicular?

Then it's not a true kite! The kite area formula $ \frac{d_1 \times d_2}{2} $ only works when the diagonals meet at 90-degree angles.

Q: Can I use this formula for any quadrilateral?

No! This formula is specifically for kites and rhombuses where diagonals are perpendicular. For other quadrilaterals, you need different area formulas.

Kite Area Formula 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

00:05 Let's find the area of the kite.

00:08 We'll use a simple formula to calculate it.

00:12 Multiply the length of one diagonal by the other, then divide by 2.

00:17 Now, let's substitute the numbers provided, and solve for the area.

00:41 And that gives us 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 the deltoid, we will use the formula for the area of a kite which is based on the lengths of its diagonals:

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

Given:

$d_1 = AC = 13$ cm, and
$d_2 = BD = 17.5$ cm.

Now, substitute these values into the formula:

$\text{Area} = \frac{13 \times 17.5}{2}$

Calculating inside the parentheses:

$13 \times 17.5 = 227.5$

Therefore, the area is:

$\text{Area} = \frac{227.5}{2} = 113.75$ cm²

The area of the deltoid ABCD is $113.75$ cm².

The correct answer choice is: $113.75$ cm².

Final Answer

$113.75$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area of kite equals half the product of diagonals
Calculation: $\frac{13 \times 17.5}{2} = \frac{227.5}{2} = 113.75$
Check: Verify diagonals are perpendicular and calculation gives 113.75 cm² ✓

Common Mistakes

Avoid these frequent errors

Using side lengths instead of diagonal lengths
Don't use the side lengths of the kite in the area formula = completely wrong result! The kite area formula specifically requires the lengths of the two diagonals that intersect inside the shape. Always identify the diagonals (lines connecting opposite vertices) and use those measurements.

Practice Quiz

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Indicate the correct answer

The next quadrilateral is:

FAQ

Everything you need to know about this question

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

A deltoid is just another name for a kite! Both are quadrilaterals with two pairs of adjacent sides that are equal and diagonals that meet at right angles.

Why do we divide by 2 in the kite area formula?

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

How do I identify which measurements are the diagonals?

Diagonals connect opposite vertices (corners) and cross inside the shape. In this problem, diagonal AC = 13 and diagonal BD = 17.5, both shown as colored lines in the diagram.

What if the diagonals aren't perpendicular?

Then it's not a true kite! The kite area formula $\frac{d_1 \times d_2}{2}$ only works when the diagonals meet at 90-degree angles.

Can I use this formula for any quadrilateral?

No! This formula is specifically for kites and rhombuses where diagonals are perpendicular. For other quadrilaterals, you need different area formulas.

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