Area of Trapezoids Practice | Worksheet - Free Printable
Educational worksheet: Area of Trapezoids Practice | Worksheet. Download and print for classroom or home learning activities.
GIF
301×385
21.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #724872
⭐
Show Answer Key & Explanations
Step-by-step solution for: Area of Trapezoids Practice | Worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Area of Trapezoids Practice | Worksheet
To solve the problem of finding the area of each trapezoid, we will use the formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
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 bases.
Let's solve each problem step by step.
---
- Bases: \(4 \, \text{cm}\) and \(7 \, \text{cm}\)
- Height: \(4 \, \text{cm}\)
\[
\text{Area} = \frac{1}{2} \times (4 + 7) \times 4 = \frac{1}{2} \times 11 \times 4 = \frac{1}{2} \times 44 = 22 \, \text{cm}^2
\]
Answer: \(22 \, \text{cm}^2\)
---
- Bases: \(11 \, \text{yd}\) and \(9 \, \text{yd}\)
- Height: \(6 \, \text{yd}\)
\[
\text{Area} = \frac{1}{2} \times (11 + 9) \times 6 = \frac{1}{2} \times 20 \times 6 = \frac{1}{2} \times 120 = 60 \, \text{yd}^2
\]
Answer: \(60 \, \text{yd}^2\)
---
- Bases: \(2 \, \text{ft}\) and \(5 \, \text{ft}\)
- Height: \(3 \, \text{ft}\)
\[
\text{Area} = \frac{1}{2} \times (2 + 5) \times 3 = \frac{1}{2} \times 7 \times 3 = \frac{1}{2} \times 21 = 10.5 \, \text{ft}^2
\]
Answer: \(10.5 \, \text{ft}^2\)
---
- Bases: \(8 \, \text{m}\) and \(5 \, \text{m}\)
- Height: \(6 \, \text{m}\)
\[
\text{Area} = \frac{1}{2} \times (8 + 5) \times 6 = \frac{1}{2} \times 13 \times 6 = \frac{1}{2} \times 78 = 39 \, \text{m}^2
\]
Answer: \(39 \, \text{m}^2\)
---
- Bases: \(10 \, \text{in}\) and \(15 \, \text{in}\)
- Height: \(9 \, \text{in}\)
\[
\text{Area} = \frac{1}{2} \times (10 + 15) \times 9 = \frac{1}{2} \times 25 \times 9 = \frac{1}{2} \times 225 = 112.5 \, \text{in}^2
\]
Answer: \(112.5 \, \text{in}^2\)
---
- Bases: \(7 \, \text{cm}\) and \(10 \, \text{cm}\)
- Height: \(4 \, \text{cm}\)
\[
\text{Area} = \frac{1}{2} \times (7 + 10) \times 4 = \frac{1}{2} \times 17 \times 4 = \frac{1}{2} \times 68 = 34 \, \text{cm}^2
\]
Answer: \(34 \, \text{cm}^2\)
---
- Bases: \(8 \, \text{ft}\) and \(12 \, \text{ft}\)
- Height: \(9 \, \text{ft}\)
\[
\text{Area} = \frac{1}{2} \times (8 + 12) \times 9 = \frac{1}{2} \times 20 \times 9 = \frac{1}{2} \times 180 = 90 \, \text{ft}^2
\]
Answer: \(90 \, \text{ft}^2\)
---
- Bases: \(12 \, \text{m}\) and \(6 \, \text{m}\)
- Height: \(4 \, \text{m}\)
\[
\text{Area} = \frac{1}{2} \times (12 + 6) \times 4 = \frac{1}{2} \times 18 \times 4 = \frac{1}{2} \times 72 = 36 \, \text{m}^2
\]
Answer: \(36 \, \text{m}^2\)
---
- Bases: \(11 \, \text{yd}\) and \(5 \, \text{yd}\)
- Height: \(8 \, \text{yd}\)
\[
\text{Area} = \frac{1}{2} \times (11 + 5) \times 8 = \frac{1}{2} \times 16 \times 8 = \frac{1}{2} \times 128 = 64 \, \text{yd}^2
\]
Answer: \(64 \, \text{yd}^2\)
---
\[
\boxed{
\begin{array}{ll}
1. & 22 \, \text{cm}^2 \\
2. & 60 \, \text{yd}^2 \\
3. & 10.5 \, \text{ft}^2 \\
4. & 39 \, \text{m}^2 \\
5. & 112.5 \, \text{in}^2 \\
6. & 34 \, \text{cm}^2 \\
7. & 90 \, \text{ft}^2 \\
8. & 36 \, \text{m}^2 \\
9. & 64 \, \text{yd}^2 \\
\end{array}
}
\]
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
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 bases.
Let's solve each problem step by step.
---
Problem 1:
- Bases: \(4 \, \text{cm}\) and \(7 \, \text{cm}\)
- Height: \(4 \, \text{cm}\)
\[
\text{Area} = \frac{1}{2} \times (4 + 7) \times 4 = \frac{1}{2} \times 11 \times 4 = \frac{1}{2} \times 44 = 22 \, \text{cm}^2
\]
Answer: \(22 \, \text{cm}^2\)
---
Problem 2:
- Bases: \(11 \, \text{yd}\) and \(9 \, \text{yd}\)
- Height: \(6 \, \text{yd}\)
\[
\text{Area} = \frac{1}{2} \times (11 + 9) \times 6 = \frac{1}{2} \times 20 \times 6 = \frac{1}{2} \times 120 = 60 \, \text{yd}^2
\]
Answer: \(60 \, \text{yd}^2\)
---
Problem 3:
- Bases: \(2 \, \text{ft}\) and \(5 \, \text{ft}\)
- Height: \(3 \, \text{ft}\)
\[
\text{Area} = \frac{1}{2} \times (2 + 5) \times 3 = \frac{1}{2} \times 7 \times 3 = \frac{1}{2} \times 21 = 10.5 \, \text{ft}^2
\]
Answer: \(10.5 \, \text{ft}^2\)
---
Problem 4:
- Bases: \(8 \, \text{m}\) and \(5 \, \text{m}\)
- Height: \(6 \, \text{m}\)
\[
\text{Area} = \frac{1}{2} \times (8 + 5) \times 6 = \frac{1}{2} \times 13 \times 6 = \frac{1}{2} \times 78 = 39 \, \text{m}^2
\]
Answer: \(39 \, \text{m}^2\)
---
Problem 5:
- Bases: \(10 \, \text{in}\) and \(15 \, \text{in}\)
- Height: \(9 \, \text{in}\)
\[
\text{Area} = \frac{1}{2} \times (10 + 15) \times 9 = \frac{1}{2} \times 25 \times 9 = \frac{1}{2} \times 225 = 112.5 \, \text{in}^2
\]
Answer: \(112.5 \, \text{in}^2\)
---
Problem 6:
- Bases: \(7 \, \text{cm}\) and \(10 \, \text{cm}\)
- Height: \(4 \, \text{cm}\)
\[
\text{Area} = \frac{1}{2} \times (7 + 10) \times 4 = \frac{1}{2} \times 17 \times 4 = \frac{1}{2} \times 68 = 34 \, \text{cm}^2
\]
Answer: \(34 \, \text{cm}^2\)
---
Problem 7:
- Bases: \(8 \, \text{ft}\) and \(12 \, \text{ft}\)
- Height: \(9 \, \text{ft}\)
\[
\text{Area} = \frac{1}{2} \times (8 + 12) \times 9 = \frac{1}{2} \times 20 \times 9 = \frac{1}{2} \times 180 = 90 \, \text{ft}^2
\]
Answer: \(90 \, \text{ft}^2\)
---
Problem 8:
- Bases: \(12 \, \text{m}\) and \(6 \, \text{m}\)
- Height: \(4 \, \text{m}\)
\[
\text{Area} = \frac{1}{2} \times (12 + 6) \times 4 = \frac{1}{2} \times 18 \times 4 = \frac{1}{2} \times 72 = 36 \, \text{m}^2
\]
Answer: \(36 \, \text{m}^2\)
---
Problem 9:
- Bases: \(11 \, \text{yd}\) and \(5 \, \text{yd}\)
- Height: \(8 \, \text{yd}\)
\[
\text{Area} = \frac{1}{2} \times (11 + 5) \times 8 = \frac{1}{2} \times 16 \times 8 = \frac{1}{2} \times 128 = 64 \, \text{yd}^2
\]
Answer: \(64 \, \text{yd}^2\)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. & 22 \, \text{cm}^2 \\
2. & 60 \, \text{yd}^2 \\
3. & 10.5 \, \text{ft}^2 \\
4. & 39 \, \text{m}^2 \\
5. & 112.5 \, \text{in}^2 \\
6. & 34 \, \text{cm}^2 \\
7. & 90 \, \text{ft}^2 \\
8. & 36 \, \text{m}^2 \\
9. & 64 \, \text{yd}^2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of area trapezoid worksheet.
