To solve the problem of finding the area of each trapezoid, we will use the formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Let's go through each trapezoid step by step.
---
Trapezoid 1:
-
Bases: \(5 \, \text{cm}\) and \(8 \, \text{cm}\)
-
Height: \(4 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (5 + 8) \times 4
\]
\[
\text{Area} = \frac{1}{2} \times 13 \times 4
\]
\[
\text{Area} = \frac{1}{2} \times 52
\]
\[
\text{Area} = 26 \, \text{cm}^2
\]
---
Trapezoid 2:
-
Bases: \(9 \, \text{cm}\) and \(12 \, \text{cm}\)
-
Height: \(6 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (9 + 12) \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 21 \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 126
\]
\[
\text{Area} = 63 \, \text{cm}^2
\]
---
Trapezoid 3:
-
Bases: \(7 \, \text{cm}\) and \(10 \, \text{cm}\)
-
Height: \(3 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (7 + 10) \times 3
\]
\[
\text{Area} = \frac{1}{2} \times 17 \times 3
\]
\[
\text{Area} = \frac{1}{2} \times 51
\]
\[
\text{Area} = 25.5 \, \text{cm}^2
\]
---
Trapezoid 4:
-
Bases: \(6 \, \text{cm}\) and \(9 \, \text{cm}\)
-
Height: \(5 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (6 + 9) \times 5
\]
\[
\text{Area} = \frac{1}{2} \times 15 \times 5
\]
\[
\text{Area} = \frac{1}{2} \times 75
\]
\[
\text{Area} = 37.5 \, \text{cm}^2
\]
---
Trapezoid 5:
-
Bases: \(12 \, \text{cm}\) and \(18 \, \text{cm}\)
-
Height: \(7 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (12 + 18) \times 7
\]
\[
\text{Area} = \frac{1}{2} \times 30 \times 7
\]
\[
\text{Area} = \frac{1}{2} \times 210
\]
\[
\text{Area} = 105 \, \text{cm}^2
\]
---
Trapezoid 6:
-
Bases: \(5 \, \text{cm}\) and \(8 \, \text{cm}\)
-
Height: \(6 \, \text{cm}\)
Using the formula:
\[
\text{Area} = \frac{1}{2} \times (5 + 8) \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 13 \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 78
\]
\[
\text{Area} = 39 \, \text{cm}^2
\]
---
Final Answers:
\[
\boxed{26, 63, 25.5, 37.5, 105, 39}
\]
Parent Tip: Review the logic above to help your child master the concept of decomposing shapes to find area worksheet.