Practice worksheet for calculating the area of rhombuses using diagonal measurements.

To find the area of a rhombus when you know the lengths of its diagonals, you use this simple formula:

Area = (Diagonal 1 × Diagonal 2) ÷ 2

Or written another way:
Area = $\frac{1}{2} \times d_1 \times d_2$

Let’s solve each problem step by step.

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Problem 1:
- $d_1 = \frac{7}{4}$ in
- $d_2 = \frac{7}{4}$ in

Multiply them:
$\frac{7}{4} \times \frac{7}{4} = \frac{49}{16}$

Now divide by 2 (or multiply by $\frac{1}{2}$):
$\frac{49}{16} \times \frac{1}{2} = \frac{49}{32}$

Convert to mixed number if needed:
$\frac{49}{32} = 1 \frac{17}{32}$

✔ Answer for #1: $\frac{49}{32}$ in² or $1 \frac{17}{32}$ in²

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Problem 2:
- $d_1 = \frac{5}{4}$ in
- $d_2 = \frac{5}{4}$ in

Multiply:
$\frac{5}{4} \times \frac{5}{4} = \frac{25}{16}$

Divide by 2:
$\frac{25}{16} \times \frac{1}{2} = \frac{25}{32}$

✔ Answer for #2: $\frac{25}{32}$ in²

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Problem 3:
- $d_1 = \frac{3}{4}$ yd
- $d_2 = \frac{9}{8}$ yd

Multiply:
$\frac{3}{4} \times \frac{9}{8} = \frac{27}{32}$

Divide by 2:
$\frac{27}{32} \times \frac{1}{2} = \frac{27}{64}$

✔ Answer for #3: $\frac{27}{64}$ yd²

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Problem 4:
- $d_1 = \frac{5}{4}$ in
- $d_2 = \frac{1}{4}$ in

Multiply:
$\frac{5}{4} \times \frac{1}{4} = \frac{5}{16}$

Divide by 2:
$\frac{5}{16} \times \frac{1}{2} = \frac{5}{32}$

✔ Answer for #4: $\frac{5}{32}$ in²

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Problem 5:
- $d_1 = \frac{5}{4}$ ft
- $d_2 = \frac{5}{4}$ ft

Same as Problem 2 but in feet.

Multiply:
$\frac{5}{4} \times \frac{5}{4} = \frac{25}{16}$

Divide by 2:
$\frac{25}{16} \times \frac{1}{2} = \frac{25}{32}$

✔ Answer for #5: $\frac{25}{32}$ ft²

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Problem 6:
- $d_1 = \frac{1}{4}$ in
- $d_2 = \frac{3}{4}$ in

Multiply:
$\frac{1}{4} \times \frac{3}{4} = \frac{3}{16}$

Divide by 2:
$\frac{3}{16} \times \frac{1}{2} = \frac{3}{32}$

✔ Answer for #6: $\frac{3}{32}$ in²

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Problem 7:
- $d_1 = \frac{7}{4}$ mi
- $d_2 = \frac{5}{4}$ mi

Multiply:
$\frac{7}{4} \times \frac{5}{4} = \frac{35}{16}$

Divide by 2:
$\frac{35}{16} \times \frac{1}{2} = \frac{35}{32}$

As mixed number: $1 \frac{3}{32}$

✔ Answer for #7: $\frac{35}{32}$ mi² or $1 \frac{3}{32}$ mi²

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Problem 8:
- $d_1 = \frac{5}{4}$ ft
- $d_2 = \frac{7}{4}$ ft

Multiply:
$\frac{5}{4} \times \frac{7}{4} = \frac{35}{16}$

Divide by 2:
$\frac{35}{16} \times \frac{1}{2} = \frac{35}{32}$

✔ Answer for #8: $\frac{35}{32}$ ft² or $1 \frac{3}{32}$ ft²

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Problem 9:
- $d_1 = \frac{3}{4}$ in
- $d_2 = \frac{5}{4}$ in

Multiply:
$\frac{3}{4} \times \frac{5}{4} = \frac{15}{16}$

Divide by 2:
$\frac{15}{16} \times \frac{1}{2} = \frac{15}{32}$

✔ Answer for #9: $\frac{15}{32}$ in²

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Final Answer:

1. $\frac{49}{32}$ in²
2. $\frac{25}{32}$ in²
3. $\frac{27}{64}$ yd²
4. $\frac{5}{32}$ in²
5. $\frac{25}{32}$ ft²
6. $\frac{3}{32}$ in²
7. $\frac{35}{32}$ mi²
8. $\frac{35}{32}$ ft²
9. $\frac{15}{32}$ in²