Problem: Calculate the areas of triangles, parallelograms, and trapezoids as shown in the worksheet.
####
Step-by-Step Solution:
---
1. Parallelogram (Problem 1)
Given:
- Base = 5
- Height = 2
Formula for the area of a parallelogram:
\[
\text{Area} = \text{Base} \times \text{Height}
\]
Calculation:
\[
\text{Area} = 5 \times 2 = 10
\]
Answer:
\[
\boxed{10}
\]
---
2. Triangle (Problem 2)
Given:
- Base = 9
- Height = 2.03
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times 9 \times 2.03 = \frac{1}{2} \times 18.27 = 9.135
\]
Answer:
\[
\boxed{9.135}
\]
---
3. Trapezoid (Problem 3)
Given:
- Top base (\(b_1\)) = 7
- Bottom base (\(b_2\)) = 16
- Height = 3.94
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Top base} + \text{Bottom base}) \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times (7 + 16) \times 3.94 = \frac{1}{2} \times 23 \times 3.94 = \frac{1}{2} \times 90.62 = 45.31
\]
Answer:
\[
\boxed{45.31}
\]
---
4. Triangle (Problem 4)
Given:
- Base = 14
- Height = 3
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times 14 \times 3 = \frac{1}{2} \times 42 = 21
\]
Answer:
\[
\boxed{21}
\]
---
5. Triangle (Problem 5)
Given:
- Base = 11
- Height = 4.50
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times 11 \times 4.50 = \frac{1}{2} \times 49.5 = 24.75
\]
Answer:
\[
\boxed{24.75}
\]
---
6. Trapezoid (Problem 6)
Given:
- Top base (\(b_1\)) = 4
- Bottom base (\(b_2\)) = 8
- Height = 2.53
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Top base} + \text{Bottom base}) \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times (4 + 8) \times 2.53 = \frac{1}{2} \times 12 \times 2.53 = \frac{1}{2} \times 30.36 = 15.18
\]
Answer:
\[
\boxed{15.18}
\]
---
Final Answers:
1. \( \boxed{10} \)
2. \( \boxed{9.135} \)
3. \( \boxed{45.31} \)
4. \( \boxed{21} \)
5. \( \boxed{24.75} \)
6. \( \boxed{15.18} \)
---
Explanation:
-
Parallelogram: The area is calculated using the formula \( \text{Base} \times \text{Height} \).
-
Triangle: The area is calculated using the formula \( \frac{1}{2} \times \text{Base} \times \text{Height} \).
-
Trapezoid: The area is calculated using the formula \( \frac{1}{2} \times (\text{Top base} + \text{Bottom base}) \times \text{Height} \).
Each step involves identifying the relevant dimensions and applying the appropriate formula.
Parent Tip: Review the logic above to help your child master the concept of area of triangle rectangle parallelogram trapezoid worksheet.
