Calculate the Diagonal DB in a Deltoid with Area 63 cm² and AC = 7

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. Its diagonals are perpendicular, and one diagonal bisects the other at right angles.

Q: Why do we use 1/2 × p × q for the area?

The deltoid area formula comes from the fact that perpendicular diagonals divide it into triangular sections. The area equals half the product of the diagonal lengths, just like finding the area of a rhombus!

Q: How do I remember which diagonal is which?

It doesn't matter! The area formula $ A = \frac{1}{2} \times p \times q $ works regardless of which diagonal you call p or q since multiplication is commutative.

Q: What if I get the wrong answer when I check my work?

Double-check your arithmetic first! Make sure you multiplied by 1/2 correctly and didn't skip any steps. If the math is right but the answer doesn't match, reread the problem carefully.

Q: Can I use this formula for any quadrilateral?

No! This formula $ A = \frac{1}{2} \times d_1 \times d_2 $ only works for quadrilaterals with perpendicular diagonals, like deltoids, rhombuses, and squares.

Deltoid Area Formula with Diagonal Calculations

Look at the deltoid ABCD below.

Diagonal AC = 7

The area of the deltoid is 63 cm².

Calculate the diagonal DB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the diagonal DB

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

00:06 (diagonal times diagonal) divided by 2

00:14 We'll substitute appropriate values according to the given data and solve for BD

00:19 We'll multiply by 2 to eliminate the fraction

00:27 We'll isolate BD

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

Look at the deltoid ABCD below.

Diagonal AC = 7

The area of the deltoid is 63 cm².

Calculate the diagonal DB.

Step-by-step solution

To solve the problem, we will apply the formula for the area of a deltoid using its diagonals.

The formula for the area $A$ of a deltoid with diagonals $p$ and $q$ is given by:

A = \frac{1}{2} \times p \times q

where $p$ and $q$ are the lengths of diagonals AC and DB, respectively.

In this problem:

Diagonal $p = AC = 7$ cm
The area $A = 63$ cm²

We need to find diagonal $q = DB$ .

Substituting the known values into the formula:

63 = \frac{1}{2} \times 7 \times DB

To isolate $DB$ , first multiply both sides by 2:

126 = 7 \times DB

Now, divide both sides by 7 to solve for $DB$ :

DB = \frac{126}{7}

Calculating this gives:

DB = 18

Therefore, the length of diagonal $DB$ is 18 cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Deltoid area equals half the product of both diagonals
Technique: Use $A = \frac{1}{2} \times p \times q$ where p and q are diagonals
Check: Verify $\frac{1}{2} \times 7 \times 18 = 63$ cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half in the area formula
Don't use A = p × q directly = doubles the actual area! This gives 126 cm² instead of 63 cm². Always include the factor of 1/2 in the deltoid area formula.

Practice Quiz

Test your knowledge with interactive questions

Look at the deltoid in the figure:

What is its area?

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. Its diagonals are perpendicular, and one diagonal bisects the other at right angles.

Why do we use 1/2 × p × q for the area?

The deltoid area formula comes from the fact that perpendicular diagonals divide it into triangular sections. The area equals half the product of the diagonal lengths, just like finding the area of a rhombus!

How do I remember which diagonal is which?

It doesn't matter! The area formula $A = \frac{1}{2} \times p \times q$ works regardless of which diagonal you call p or q since multiplication is commutative.

What if I get the wrong answer when I check my work?

Double-check your arithmetic first! Make sure you multiplied by 1/2 correctly and didn't skip any steps. If the math is right but the answer doesn't match, reread the problem carefully.

Can I use this formula for any quadrilateral?

No! This formula $A = \frac{1}{2} \times d_1 \times d_2$ only works for quadrilaterals with perpendicular diagonals, like deltoids, rhombuses, and squares.

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Calculate the Diagonal DB in a Deltoid with Area 63 cm² and AC = 7

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 1/2 × p × q for the area?

How do I remember which diagonal is which?

What if I get the wrong answer when I check my work?

Can I use this formula for any quadrilateral?

🌟 Unlock Your Math Potential

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