Calculate the Area of a Deltoid: 8x11 Unit Dimensions Problem

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

A deltoid (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals, which is why we can use the simple diagonal formula!

Q: Why do we multiply by 1/2 in the area formula?

The diagonals of a deltoid divide it into 4 right triangles. When you multiply the full diagonal lengths, you get double the actual area, so we divide by 2 to get the correct result.

Q: How can I identify which measurements are the diagonals?

Diagonals are the lines that connect opposite vertices and cross inside the shape. In this problem, the vertical line (8 cm) and horizontal line (11 cm) are clearly marked as the diagonals.

Q: What if the diagonals aren't perpendicular?

If the diagonals aren't perpendicular, then it's not a deltoid! The $ A = \frac{1}{2} \times d_1 \times d_2 $ formula only works when diagonals meet at right angles, which is a key property of deltoids.

Q: Can I use this formula for any kite-shaped figure?

Yes! This diagonal formula works for all kites and deltoids because they all have perpendicular diagonals. Just make sure you're measuring the full length of each diagonal, not just half-segments.

Deltoid Area with Diagonal Measurements

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

00:03 Let's find the area of the kite.

00:07 We will use a simple formula to calculate its area.

00:12 Multiply the length of one diagonal by the other. Then, divide by 2.

00:17 Next, substitute the given values into the formula and solve for the area.

00:31 First, divide 8 by 2.

00:40 And that's how we find the solution to this problem!

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 this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Use the appropriate formula for area calculation.
Step 3: Perform the calculation using the formula.

Now, let's work through each step:
Step 1: We recognize that the vertical diagonal $AC = 8$ cm and the horizontal diagonal $BD = 11$ cm.
Step 2: We'll use the formula for the area of a deltoid (kite), given by
$A = \frac{1}{2} \times d_1 \times d_2$ , where $d_1$ and $d_2$ are the lengths of the diagonals.
Step 3: Plugging in our values, we get:
$A = \frac{1}{2} \times 8 \times 11$
$A = \frac{1}{2} \times 88$
$A = 44$ cm².

Thus, the area of the deltoid is $44$ cm².

Final Answer

$44$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half the product of both diagonals
Technique: Use $A = \frac{1}{2} \times 8 \times 11 = 44$ cm²
Check: Verify diagonals are perpendicular and calculation: $\frac{88}{2} = 44$ ✓

Common Mistakes

Avoid these frequent errors

Using side lengths instead of diagonal lengths
Don't measure the sides of the deltoid and multiply them = wrong formula! This gives you a rectangle area, not a deltoid area. Always identify and use the diagonal measurements with the formula $A = \frac{1}{2} \times d_1 \times d_2$ .

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 (also called a kite) is a quadrilateral with two pairs of adjacent sides that are equal. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals, which is why we can use the simple diagonal formula!

Why do we multiply by 1/2 in the area formula?

The diagonals of a deltoid divide it into 4 right triangles. When you multiply the full diagonal lengths, you get double the actual area, so we divide by 2 to get the correct result.

How can I identify which measurements are the diagonals?

Diagonals are the lines that connect opposite vertices and cross inside the shape. In this problem, the vertical line (8 cm) and horizontal line (11 cm) are clearly marked as the diagonals.

What if the diagonals aren't perpendicular?

If the diagonals aren't perpendicular, then it's not a deltoid! The $A = \frac{1}{2} \times d_1 \times d_2$ formula only works when diagonals meet at right angles, which is a key property of deltoids.

Can I use this formula for any kite-shaped figure?

Yes! This diagonal formula works for all kites and deltoids because they all have perpendicular diagonals. Just make sure you're measuring the full length of each diagonal, not just half-segments.

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