To solve this worksheet, we need to calculate the
area of each trapezium using the formula:
$$
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
$$
Where:
- $\text{Base}_1$ and $\text{Base}_2$ are the lengths of the two parallel sides (top and bottom),
- Height is the perpendicular distance between the two bases.
Let’s go through each trapezium one by one.
---
1. First Trapezium
- Top base = 7
- Bottom base = 9
- Height = 8
$$
\text{Area} = \frac{1}{2} \times (7 + 9) \times 8 = \frac{1}{2} \times 16 \times 8 = 8 \times 8 = 64
$$
✔ Area = 64
---
2. Second Trapezium
- Top base = 9
- Bottom base = 11
- Height = 12
$$
\text{Area} = \frac{1}{2} \times (9 + 11) \times 12 = \frac{1}{2} \times 20 \times 12 = 10 \times 12 = 120
$$
✔ Area = 120
---
3. Third Trapezium
- Top base = 6
- Bottom base = 12
- Height = 4
$$
\text{Area} = \frac{1}{2} \times (6 + 12) \times 4 = \frac{1}{2} \times 18 \times 4 = 9 \times 4 = 36
$$
✔ Area = 36
---
4. Fourth Trapezium
- Top base = 2
- Bottom base = 3
- Height = 1
$$
\text{Area} = \frac{1}{2} \times (2 + 3) \times 1 = \frac{1}{2} \times 5 \times 1 = 2.5
$$
✔ Area = 2.5
---
5. Fifth Trapezium
- Top base = 6
- Bottom base = 10
- Height = 7
$$
\text{Area} = \frac{1}{2} \times (6 + 10) \times 7 = \frac{1}{2} \times 16 \times 7 = 8 \times 7 = 56
$$
✔ Area = 56
---
6. Sixth Trapezium
- Top base = 3
- Bottom base = 8
- Height = 2
$$
\text{Area} = \frac{1}{2} \times (3 + 8) \times 2 = \frac{1}{2} \times 11 \times 2 = 11
$$
✔ Area = 11
---
✔ Final Answers:
1.
64
2.
120
3.
36
4.
2.5
5.
56
6.
11
---
🔍 Explanation:
The key idea is that a trapezium has
two parallel sides, and the area depends on the
average of those two bases multiplied by the
height (perpendicular distance). This formula works regardless of whether the non-parallel sides are slanted or not — as long as you have the height and the two base lengths.
You can remember it as:
> "Average of the two bases times the height."
This method applies to all six problems here.
Let me know if you'd like a visual explanation or printable version!
Parent Tip: Review the logic above to help your child master the concept of trapezoid area worksheet.
