Calculate the Area of Deltoid ABCD with Height 5 and Base 18

Q: Why do we use diagonals instead of sides to find kite area?

Kite diagonals are perpendicular (meet at 90°), which creates four right triangles inside. The diagonal 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 connect opposite vertices of the kite and cross each other inside the shape. In this problem, AC = 5 and BD = 18 are the diagonals, not the sides of the kite.

Q: What if the diagonals aren't perpendicular?

Then it's not a true kite! By definition, a kite's diagonals must be perpendicular. If they're not, you'd need a different area formula for that quadrilateral.

Q: Can I use this formula for any quadrilateral?

No! This formula $ \frac{1}{2} \times d_1 \times d_2 $ only works for shapes with perpendicular diagonals like kites, rhombuses, and squares. Other quadrilaterals need different formulas.

Q: Do I need to know all four side lengths?

Not for area! You only need the diagonal lengths for a kite's area. Side lengths would be needed for perimeter, but not for this calculation.

Kite Area with Perpendicular Diagonals

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

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

00:23 Divide 18 by 2

00:33 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

We are tasked with finding the area of the deltoid (or kite) ABCD using the lengths of its diagonals. The given diagonals are $AC = 5$ cm and $BD = 18$ cm. The diagonals of a kite are perpendicular to each other.

To find the area of the kite, we use the formula:

$\text{Area} = \frac{1}{2} \times d_1 \times d_2$

Substituting the given values ( $d_1 = 5$ cm and $d_2 = 18$ cm) into the formula, we get:

$\text{Area} = \frac{1}{2} \times 5 \times 18 = \frac{1}{2} \times 90 = 45 \text{ cm}^2$

Hence, the area of the deltoid ABCD is $45$ cm².

Final Answer

$45$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area of kite equals half the product of diagonal lengths
Calculation: $\frac{1}{2} \times 5 \times 18 = 45$ square units
Check: Verify diagonals are perpendicular and formula gives reasonable answer ✓

Common Mistakes

Avoid these frequent errors

Using base times height instead of diagonal formula
Don't treat a kite like a triangle using base × height ÷ 2 = wrong area! A kite's "height" and "base" don't work the same way as triangles. Always use the kite formula: ½ × diagonal₁ × diagonal₂.

Practice Quiz

Test your knowledge with interactive questions

Look at the kite ABCD below.

Diagonal DB = 10

CB = 4

Is it possible to calculate the area of the kite? If so, what is it?

FAQ

Everything you need to know about this question

Why do we use diagonals instead of sides to find kite area?

Kite diagonals are perpendicular (meet at 90°), which creates four right triangles inside. The diagonal 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 connect opposite vertices of the kite and cross each other inside the shape. In this problem, AC = 5 and BD = 18 are the diagonals, not the sides of the kite.

What if the diagonals aren't perpendicular?

Then it's not a true kite! By definition, a kite's diagonals must be perpendicular. If they're not, you'd need a different area formula for that quadrilateral.

Can I use this formula for any quadrilateral?

No! This formula $\frac{1}{2} \times d_1 \times d_2$ only works for shapes with perpendicular diagonals like kites, rhombuses, and squares. Other quadrilaterals need different formulas.

Do I need to know all four side lengths?

Not for area! You only need the diagonal lengths for a kite's area. Side lengths would be needed for perimeter, but not for this calculation.

🌟 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