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

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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

Indicate the correct answer

The next quadrilateral is:

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.

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