Deltoid Area Problem: Solve for X When Area = 16 cm² and Length = 2×Width

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

A deltoid is a special quadrilateral that looks like a kite! It has two pairs of adjacent sides that are equal in length. The key feature is that its diagonals are perpendicular, which is why we can use the simple area formula.

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

Diagonals are the lines that connect opposite vertices (corners) of the deltoid. In this problem, the diagram shows the vertical line (2x) and horizontal line (x) crossing inside the shape - these are your diagonals!

Q: Why does the area formula use 1/2 times the diagonals?

When diagonals are perpendicular (form 90° angles), they divide the deltoid into 4 right triangles. The formula $ A = \frac{1}{2} \times d_1 \times d_2 $ calculates the total area of all four triangles together.

Q: What if I get a negative value when solving x² = 16?

Great observation! Mathematically $ x = ±4 $, but since we're measuring length, we only use the positive value. Distances can't be negative in geometry problems!

Q: Can I use this same method for other kite-shaped figures?

Yes! This area formula works for any quadrilateral with perpendicular diagonals - including kites, rhombuses, and squares. Just make sure the diagonals actually cross at right angles.

Deltoid Area Formula with Diagonal Relationships

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate X

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

00:09 (diagonal times diagonal) divided by 2

00:13 We'll substitute appropriate values according to the given data and find X

00:24 We'll simplify what we can

00:30 Extract the root

00:42 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

Step-by-step solution

Given the problem, we are tasked to find the value of $x$ for a deltoid where the length is twice the width and the area is given. Let's proceed as follows:

Step 1: In this deltoid problem, the diagonals correspond to length $2x$ and width $x$ . The formula for the area of a deltoid in terms of its diagonals is $A = \frac{1}{2} \times d_1 \times d_2$ .
Step 2: Substitute the values. Thus, the area $16 = \frac{1}{2} \times (2x) \times x$ .
Step 3: Simplify the equation: $16 = \frac{1}{2} \times 2x^2 = x^2$ .
Step 4: Solve for $x$ : We find $x^2 = 16$ , so $x = \sqrt{16}$ .
Step 5: Conclude $x = 4$ .

Therefore, the solution to the problem is $x = 4$ .

Final Answer

$x=4$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of deltoid equals half the product of diagonal lengths
Technique: Set up $16 = \frac{1}{2} \times (2x) \times x = x^2$
Check: Verify diagonals 8 and 4 give area: $\frac{1}{2} \times 8 \times 4 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Using side lengths instead of diagonal lengths in area formula
Don't substitute side measurements into the area formula = completely wrong calculation! The deltoid area formula specifically requires the two diagonal lengths, not the sides. Always identify which measurements are diagonals before applying $A = \frac{1}{2} \times d_1 \times d_2$ .

Practice Quiz

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Indicate the correct answer

The next quadrilateral is:

FAQ

Everything you need to know about this question

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

A deltoid is a special quadrilateral that looks like a kite! It has two pairs of adjacent sides that are equal in length. The key feature is that its diagonals are perpendicular, which is why we can use the simple area formula.

How do I know which measurements are the diagonals?

Diagonals are the lines that connect opposite vertices (corners) of the deltoid. In this problem, the diagram shows the vertical line (2x) and horizontal line (x) crossing inside the shape - these are your diagonals!

Why does the area formula use 1/2 times the diagonals?

When diagonals are perpendicular (form 90° angles), they divide the deltoid into 4 right triangles. The formula $A = \frac{1}{2} \times d_1 \times d_2$ calculates the total area of all four triangles together.

What if I get a negative value when solving x² = 16?

Great observation! Mathematically $x = ±4$ , but since we're measuring length, we only use the positive value. Distances can't be negative in geometry problems!

Can I use this same method for other kite-shaped figures?

Yes! This area formula works for any quadrilateral with perpendicular diagonals - including kites, rhombuses, and squares. Just make sure the diagonals actually cross at right angles.

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Deltoid Area Problem: Solve for X When Area = 16 cm² and Length = 2×Width

Deltoid Area Formula with Diagonal Relationships

❤️ 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?

How do I know which measurements are the diagonals?

Why does the area formula use 1/2 times the diagonals?

What if I get a negative value when solving x² = 16?

Can I use this same method for other kite-shaped figures?

🌟 Unlock Your Math Potential

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