Calculate the Area of Deltoid ABCD with Height 5 and Base 9

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

A deltoid (or kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals that intersect, making the diagonal formula perfect for finding area!

Q: Why do we multiply the diagonals and divide by 2?

When diagonals are perpendicular, they split the deltoid into four right triangles. The formula $ \frac{1}{2} \times d_1 \times d_2 $ efficiently calculates the total area of all four triangles at once!

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

Diagonals are the lines connecting opposite vertices (corners). In this problem, AC = 5 and BD = 9 are diagonals because they connect opposite points and cross inside the shape.

Q: What if I accidentally add the diagonals instead of multiplying?

Adding gives you 5 + 9 = 14, but that's the perimeter of a rectangle, not area! Always remember: area formulas use multiplication, while perimeter uses addition.

Q: Can I use this formula for any quadrilateral?

No! This formula only works when diagonals are perpendicular (meet at 90°). For other quadrilaterals like rectangles or parallelograms, you need different area formulas.

Deltoid Area with Diagonal Lengths

Given the deltoid ABCD

Find the area

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 area of the kite

00:07 (diagonal times diagonal) divided by 2

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

00:29 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 can apply the following method:

Step 1: Identify the diagonals:
From the problem, $AC = 5$ cm and $BD = 9$ cm are the lengths of the diagonals.
Step 2: Apply the area of deltoid formula:
When diagonals intersect perpendicularly in a kite or deltoid shape, the area $A$ is given by:
$A = \frac{1}{2} \times d_1 \times d_2$
where $d_1 = 5$ cm and $d_2 = 9$ cm are the diagonals.
Step 3: Substitute and calculate:
$A = \frac{1}{2} \times 5 \times 9$
$A = \frac{1}{2} \times 45$
$A = 22.5$ cm²

Therefore, the area of the deltoid ABCD is $22.5$ cm².

Final Answer

$22.5$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Deltoid area equals one-half times diagonal product
Technique: Area = $\frac{1}{2} \times 5 \times 9 = 22.5$ cm²
Check: Verify perpendicular diagonals and multiply correctly: $\frac{45}{2} = 22.5$ ✓

Common Mistakes

Avoid these frequent errors

Confusing diagonal formula with regular triangle area
Don't use Area = $\frac{1}{2} \times base \times height$ for deltoids = wrong answer of 12.5! This ignores the kite's unique diagonal structure. Always use Area = $\frac{1}{2} \times d_1 \times d_2$ when diagonals are perpendicular.

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 exactly is a deltoid and how is it different from other shapes?

A deltoid (or kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals that intersect, making the diagonal formula perfect for finding area!

Why do we multiply the diagonals and divide by 2?

When diagonals are perpendicular, they split the deltoid into four right triangles. The formula $\frac{1}{2} \times d_1 \times d_2$ efficiently calculates the total area of all four triangles at once!

How do I know which measurements are the diagonals?

Diagonals are the lines connecting opposite vertices (corners). In this problem, AC = 5 and BD = 9 are diagonals because they connect opposite points and cross inside the shape.

What if I accidentally add the diagonals instead of multiplying?

Adding gives you 5 + 9 = 14, but that's the perimeter of a rectangle, not area! Always remember: area formulas use multiplication, while perimeter uses addition.

Can I use this formula for any quadrilateral?

No! This formula only works when diagonals are perpendicular (meet at 90°). For other quadrilaterals like rectangles or parallelograms, you need different area formulas.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Deltoid questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime