Problem: Calculate the areas of triangles, parallelograms, and trapezoids from the given worksheet.
####
Step-by-Step Solution:
---
1. Triangle (Problem 1)
Given:
- Base = 14
- Height = 5.25
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times 14 \times 5.25 = 7 \times 5.25 = 36.75
\]
Answer:
\[
\boxed{36.75}
\]
---
2. Trapezoid (Problem 2)
Given:
- Bases = 5.63 and 6
- Height = 3
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times (5.63 + 6) \times 3 = \frac{1}{2} \times 11.63 \times 3 = 5.815 \times 3 = 17.445
\]
Answer:
\[
\boxed{17.445}
\]
---
3. Parallelogram (Problem 3)
Given:
- Base = 5
- Height = 3.01
Formula for the area of a parallelogram:
\[
\text{Area} = \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = 5 \times 3.01 = 15.05
\]
Answer:
\[
\boxed{15.05}
\]
---
4. Parallelogram (Problem 4)
Given:
- Base = 5
- Height = 4.65
Formula for the area of a parallelogram:
\[
\text{Area} = \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = 5 \times 4.65 = 23.25
\]
Answer:
\[
\boxed{23.25}
\]
---
5. Trapezoid (Problem 5)
Given:
- Bases = 3.30 and 13
- Height = 6
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times (3.30 + 13) \times 6 = \frac{1}{2} \times 16.30 \times 6 = 8.15 \times 6 = 48.9
\]
Answer:
\[
\boxed{48.9}
\]
---
6. Parallelogram (Problem 6)
Given:
- Base = 11
- Height = 4
Formula for the area of a parallelogram:
\[
\text{Area} = \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = 11 \times 4 = 44
\]
Answer:
\[
\boxed{44}
\]
---
Final Answers:
1. \(\boxed{36.75}\)
2. \(\boxed{17.445}\)
3. \(\boxed{15.05}\)
4. \(\boxed{23.25}\)
5. \(\boxed{48.9}\)
6. \(\boxed{44}\)
---
Explanation:
-
Triangles: Use the formula \(\frac{1}{2} \times \text{base} \times \text{height}\).
-
Parallelograms: Use the formula \(\text{base} \times \text{height}\).
-
Trapezoids: Use the formula \(\frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}\).
Each step involves identifying the correct dimensions (base, height, or bases) and applying the appropriate formula. The calculations are straightforward but require careful attention to decimal places.
Parent Tip: Review the logic above to help your child master the concept of area of triangles and trapezoids worksheet.
