Deltoid Area Problem: Calculate Side AC Given Area 32cm² and Diagonal DB=4

Q: What exactly is a deltoid and how is it different from other quadrilaterals?

A deltoid (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals, which is why we use the special area formula.

Q: Why do we use the diagonal formula instead of base times height?

For deltoids, the diagonals are perpendicular and intersect at right angles. This makes $ A = \frac{1}{2} \times d_1 \times d_2 $ the most efficient formula. Finding base and height would be much more complicated!

Q: How do I know which diagonal is which in the formula?

It doesn't matter! Since we're multiplying the diagonals together, DB × AC = AC × DB. You can assign either diagonal as $ d_1 $ or $ d_2 $ in the formula.

Q: What if I get a decimal answer instead of a whole number?

That's completely normal! Many geometry problems have decimal or fractional answers. Just make sure to show your work clearly and double-check by substituting back into the area formula.

Q: Can I use this same formula for other quadrilaterals like rectangles?

No! This diagonal formula only works for deltoids and rhombuses because their diagonals are perpendicular. For rectangles, use length × width. For triangles, use $ \frac{1}{2} \times base \times height $.

Deltoid Area Formula with Diagonal Calculations

Given the deltoid ABCD

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate AC

00:03 We'll use the formula for calculating the area of a kite

00:07 (diagonal times diagonal) divided by 2

00:18 We'll substitute appropriate values according to the given data and find AC

00:22 We'll multiply by 2 to eliminate the fraction

00:31 We'll isolate AC

00:37 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

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

Step-by-step solution

To solve for $AC$ in the deltoid, use the area formula:

Step 1: The area of a deltoid is given by $A = \frac{1}{2} \times p \times q$ , where $p$ and $q$ are diagonals.
Step 2: For this problem, set $p = DB = 4$ cm, and $q = AC$ (unknown).
Step 3: Substitute the values: $32 = \frac{1}{2} \times 4 \times AC$ .

Now, solve for $AC$ :
$32 = \frac{1}{2} \times 4 \times AC$
$32 = 2 \times AC$
Divide both sides by 2:
$AC = \frac{32}{2} = 16 \, \text{cm}$

The side $AC$ is therefore 16 cm.

Final Answer

16 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area of deltoid equals half times product of diagonals
Technique: Substitute known values: $32 = \frac{1}{2} \times 4 \times AC$
Check: Verify by substituting AC = 16: $\frac{1}{2} \times 4 \times 16 = 32$ ✓

Common Mistakes

Avoid these frequent errors

Using deltoid area formula incorrectly
Don't confuse deltoid area with rectangle area using length × width = wrong formula! This gives completely incorrect results because deltoids need the diagonal formula. Always use $A = \frac{1}{2} \times d_1 \times d_2$ for deltoids.

Practice Quiz

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Indicate the correct answer

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FAQ

Everything you need to know about this question

What exactly is a deltoid and how is it different from other quadrilaterals?

A deltoid (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals, which is why we use the special area formula.

Why do we use the diagonal formula instead of base times height?

For deltoids, the diagonals are perpendicular and intersect at right angles. This makes $A = \frac{1}{2} \times d_1 \times d_2$ the most efficient formula. Finding base and height would be much more complicated!

How do I know which diagonal is which in the formula?

It doesn't matter! Since we're multiplying the diagonals together, DB × AC = AC × DB. You can assign either diagonal as $d_1$ or $d_2$ in the formula.

What if I get a decimal answer instead of a whole number?

That's completely normal! Many geometry problems have decimal or fractional answers. Just make sure to show your work clearly and double-check by substituting back into the area formula.

Can I use this same formula for other quadrilaterals like rectangles?

No! This diagonal formula only works for deltoids and rhombuses because their diagonals are perpendicular. For rectangles, use length × width. For triangles, use $\frac{1}{2} \times base \times height$ .

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Deltoid Area Problem: Calculate Side AC Given Area 32cm² and Diagonal DB=4

Deltoid Area Formula with Diagonal Calculations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What exactly is a deltoid and how is it different from other quadrilaterals?

Why do we use the diagonal formula instead of base times height?

How do I know which diagonal is which in the formula?

What if I get a decimal answer instead of a whole number?

Can I use this same formula for other quadrilaterals like rectangles?

🌟 Unlock Your Math Potential

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