To solve this worksheet, we need to
calculate the area of each rhombus using the given diagonals.
🔷 Formula for the Area of a Rhombus:
The area of a rhombus can be calculated using the formula:
$$
\text{Area} = \frac{1}{2} \times d_1 \times d_2
$$
Where:
- $d_1$ and $d_2$ are the lengths of the diagonals.
---
Let's go through each rhombus one by one.
---
✔ Rhombus 1
- Diagonals: $d_1 = 8$, $d_2 = 10$
$$
\text{Area} = \frac{1}{2} \times 8 \times 10 = \frac{1}{2} \times 80 = 40
$$
✔ Area = 40
---
✔ Rhombus 2
- Diagonals: $d_1 = 5$, $d_2 = 12$
$$
\text{Area} = \frac{1}{2} \times 5 \times 12 = \frac{1}{2} \times 60 = 30
$$
✔ Area = 30
---
✔ Rhombus 3
- Diagonals: $d_1 = 3$, $d_2 = 9$
$$
\text{Area} = \frac{1}{2} \times 3 \times 9 = \frac{1}{2} \times 27 = 13.5
$$
✔ Area = 13.5
---
✔ Rhombus 4
- Diagonals: $d_1 = 2$, $d_2 = 8$
$$
\text{Area} = \frac{1}{2} \times 2 \times 8 = \frac{1}{2} \times 16 = 8
$$
✔ Area = 8
---
✔ Rhombus 5
- Diagonals: $d_1 = 7$, $d_2 = 15$
$$
\text{Area} = \frac{1}{2} \times 7 \times 15 = \frac{1}{2} \times 105 = 52.5
$$
✔ Area = 52.5
---
✔ Rhombus 6
- Diagonals: $d_1 = 10$, $d_2 = 20$
$$
\text{Area} = \frac{1}{2} \times 10 \times 20 = \frac{1}{2} \times 200 = 100
$$
✔ Area = 100
---
✔ Final Answers:
1.
40
2.
30
3.
13.5
4.
8
5.
52.5
6.
100
---
📝 Explanation:
Each rhombus has two diagonals drawn (dashed lines), which intersect at right angles and bisect each other. The area is always half the product of the diagonals because the rhombus can be divided into four right triangles, or thought of as two congruent triangles formed by one diagonal, and so on.
This method works universally for any rhombus when the diagonals are known.
Let me know if you'd like this in printable format or with steps shown!
Parent Tip: Review the logic above to help your child master the concept of area of rhombus worksheet.
