To solve this problem, we need to find the
area of each rhombus using the formula:
$$
\text{Area} = \text{base} \times \text{height} \quad \text{(or } b \times h\text{)}
$$
This formula works because a rhombus is a type of parallelogram, and the area of any parallelogram is given by base times height.
Let’s go through each rhombus one by one.
---
1. First Rhombus
- Base $ b = 4 $ cm
- Height $ h = 3 $ cm
$$
\text{Area} = 4 \times 3 = 12 \text{ cm}^2
$$
---
2. Second Rhombus
- Base $ b = 6 $ cm
- Height $ h = 5 $ cm
$$
\text{Area} = 6 \times 5 = 30 \text{ cm}^2
$$
---
3. Third Rhombus
- Base $ b = 9 $ cm
- Height $ h = 8 $ cm
$$
\text{Area} = 9 \times 8 = 72 \text{ cm}^2
$$
---
4. Fourth Rhombus
- Base $ b = 7 $ cm
- Height $ h = 6 $ cm
$$
\text{Area} = 7 \times 6 = 42 \text{ cm}^2
$$
---
5. Fifth Rhombus
- Base $ b = 4 $ cm
- Height $ h = 4.5 $ cm
$$
\text{Area} = 4 \times 4.5 = 18 \text{ cm}^2
$$
---
6. Sixth Rhombus
- Base $ b = 2 $ cm
- Height $ h = 2.5 $ cm
$$
\text{Area} = 2 \times 2.5 = 5 \text{ cm}^2
$$
---
7. Seventh Rhombus
- Base $ b = 6.5 $ cm
- Height $ h = 6 $ cm
$$
\text{Area} = 6.5 \times 6 = 39 \text{ cm}^2
$$
---
8. Eighth Rhombus
- Base $ b = 8 $ cm
- Height $ h = 7 $ cm
$$
\text{Area} = 8 \times 7 = 56 \text{ cm}^2
$$
---
9. Ninth Rhombus
- Base $ b = 8 $ cm
- Height $ h = 3.5 $ cm
$$
\text{Area} = 8 \times 3.5 = 28 \text{ cm}^2
$$
---
✔ Final Answers (in order):
1.
12 cm²
2.
30 cm²
3.
72 cm²
4.
42 cm²
5.
18 cm²
6.
5 cm²
7.
39 cm²
8.
56 cm²
9.
28 cm²
---
🔍 Explanation:
The key idea is that
the area of a rhombus (like any parallelogram) is calculated using:
$$
\text{Area} = \text{base} \times \text{height}
$$
where:
- The
base is the length of one side.
- The
height is the perpendicular distance from the base to the opposite side (not the slant height).
Even though the rhombuses are drawn at different angles, as long as you use the correct base and the corresponding perpendicular height, the formula works perfectly.
Let me know if you'd like a visual explanation or help with another method (like using diagonals)!
Parent Tip: Review the logic above to help your child master the concept of area of rhombus worksheet.
