To calculate the area of a trapezium, we use 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.
- \(\text{Height}\) is the perpendicular distance between the two parallel sides.
Let's solve each trapezium step by step.
Trapezium 1:
- \(\text{Base}_1 = 7\)
- \(\text{Base}_2 = 9\)
- \(\text{Height} = 8\)
\[
\text{Area} = \frac{1}{2} \times (7 + 9) \times 8 = \frac{1}{2} \times 16 \times 8 = 8 \times 8 = 64
\]
Trapezium 2:
- \(\text{Base}_1 = 9\)
- \(\text{Base}_2 = 11\)
- \(\text{Height} = 12\)
\[
\text{Area} = \frac{1}{2} \times (9 + 11) \times 12 = \frac{1}{2} \times 20 \times 12 = 10 \times 12 = 120
\]
Trapezium 3:
- \(\text{Base}_1 = 6\)
- \(\text{Base}_2 = 12\)
- \(\text{Height} = 4\)
\[
\text{Area} = \frac{1}{2} \times (6 + 12) \times 4 = \frac{1}{2} \times 18 \times 4 = 9 \times 4 = 36
\]
Trapezium 4:
- \(\text{Base}_1 = 2\)
- \(\text{Base}_2 = 3\)
- \(\text{Height} = 1\)
\[
\text{Area} = \frac{1}{2} \times (2 + 3) \times 1 = \frac{1}{2} \times 5 \times 1 = 2.5
\]
Trapezium 5:
- \(\text{Base}_1 = 6\)
- \(\text{Base}_2 = 10\)
- \(\text{Height} = 7\)
\[
\text{Area} = \frac{1}{2} \times (6 + 10) \times 7 = \frac{1}{2} \times 16 \times 7 = 8 \times 7 = 56
\]
Trapezium 6:
- \(\text{Base}_1 = 3\)
- \(\text{Base}_2 = 8\)
- \(\text{Height} = 2\)
\[
\text{Area} = \frac{1}{2} \times (3 + 8) \times 2 = \frac{1}{2} \times 11 \times 2 = 5.5 \times 2 = 11
\]
Final Answers:
\[
\boxed{64, 120, 36, 2.5, 56, 11}
\]
Parent Tip: Review the logic above to help your child master the concept of area of a trapezoid worksheet.
