Area of triangles, parallelograms & trapezoids - Grade 6 Geometry Worksheet

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 and applying the appropriate formula. The calculations are straightforward but require careful attention to decimal places.