Calculate the Area of a Rhombus with Diagonals 4 and 7 Units

Q: Why do we divide by 2 in the diagonal formula?

The diagonal formula $ \frac{d_1 \times d_2}{2} $ comes from the fact that a rhombus can be divided into four right triangles. Each triangle has area $ \frac{1}{2} \times \frac{d_1}{2} \times \frac{d_2}{2} $, and multiplying by 4 gives us the total area.

Q: Can I use the side × height formula instead?

Yes, but only if you know both the side length and the perpendicular height. Since this problem gives you diagonal lengths (4 and 7), the diagonal formula is much easier to use!

Q: Does it matter which diagonal I call d₁ or d₂?

No! Since we're multiplying the diagonals together, $ 7 \times 4 = 4 \times 7 = 28 $. The order doesn't change the final answer.

Q: What if I got 28 as my answer?

You forgot the most important step! $ 7 \times 4 = 28 $ is correct, but you must divide by 2 to get the area: $ \frac{28}{2} = 14 $.

Rhombus Area with Diagonal Measurements

Given the rhombus in the drawing:

What is 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 rhombus

00:03 We will use the formula to calculate the area of a rhombus

00:08 (diagonal multiplied by diagonal) divided by 2

00:14 We will substitute appropriate values and solve to find the area

00:25 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the rhombus in the drawing:

What is the area?

Step-by-step solution

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

$\frac{7\times4}{2}=\frac{28}{2}=14$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals diagonal₁ × diagonal₂ divided by 2
Calculation: $\frac{7 \times 4}{2} = \frac{28}{2} = 14$
Check: Verify diagonals are perpendicular and bisect each other in rhombus ✓

Common Mistakes

Avoid these frequent errors

Adding diagonals instead of multiplying
Don't calculate 7 + 4 = 11! Adding diagonals gives the wrong area formula and completely incorrect results. Always multiply the diagonals first, then divide by 2 for rhombus area.

Practice Quiz

Test your knowledge with interactive questions

Given the rhombus in the figure

What is your area?

FAQ

Everything you need to know about this question

Why do we divide by 2 in the diagonal formula?

The diagonal formula $\frac{d_1 \times d_2}{2}$ comes from the fact that a rhombus can be divided into four right triangles. Each triangle has area $\frac{1}{2} \times \frac{d_1}{2} \times \frac{d_2}{2}$ , and multiplying by 4 gives us the total area.

Can I use the side × height formula instead?

Yes, but only if you know both the side length and the perpendicular height. Since this problem gives you diagonal lengths (4 and 7), the diagonal formula is much easier to use!

How do I know which numbers are the diagonals?

In the diagram, the diagonals are the lines that cross through the center of the rhombus. One diagonal is labeled 4 (vertical) and the other is labeled 7 (horizontal).

Does it matter which diagonal I call d₁ or d₂?

No! Since we're multiplying the diagonals together, $7 \times 4 = 4 \times 7 = 28$ . The order doesn't change the final answer.

What if I got 28 as my answer?

You forgot the most important step! $7 \times 4 = 28$ is correct, but you must divide by 2 to get the area: $\frac{28}{2} = 14$ .

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