Area of Parallelograms, Triangles, and Trapezoids Assessment worksheet with 12 problems involving geometric shapes and their areas.

To solve the problems related to finding the areas of various shapes, we will use the appropriate formulas for each shape. Let's go through each problem step by step.

---

Formulas Needed:

1. Rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]

2. Square:
\[
\text{Area} = \text{side}^2
\]

3. Parallelogram:
\[
\text{Area} = \text{base} \times \text{height}
\]

4. Triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

5. Trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
\]

6. Rhombus:
\[
\text{Area} = \text{base} \times \text{height}
\]

---

Solutions:

#### 1. Find the area of a rectangle with dimensions 3 cm and 5 cm.
\[
\text{Area} = \text{length} \times \text{width} = 3 \, \text{cm} \times 5 \, \text{cm} = 15 \, \text{cm}^2
\]

#### 2. Find the area of a square that has a side length of 3 m.
\[
\text{Area} = \text{side}^2 = 3 \, \text{m} \times 3 \, \text{m} = 9 \, \text{m}^2
\]

#### 3. Find the area of a parallelogram with a base of 55 in and a height of 18 in.
\[
\text{Area} = \text{base} \times \text{height} = 55 \, \text{in} \times 18 \, \text{in} = 990 \, \text{in}^2
\]

#### 4. Find the area of a triangle with a base of 2 cm and a height of 6 cm.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \, \text{cm} \times 6 \, \text{cm} = 6 \, \text{cm}^2
\]

#### 5. Find the area of a rectangle with dimensions 3 m and 4 m.
\[
\text{Area} = \text{length} \times \text{width} = 3 \, \text{m} \times 4 \, \text{m} = 12 \, \text{m}^2
\]

#### 6. Find the area of a parallelogram with a base of 7 cm and a height of 8 cm.
\[
\text{Area} = \text{base} \times \text{height} = 7 \, \text{cm} \times 8 \, \text{cm} = 56 \, \text{cm}^2
\]

#### 7. Find the area of a triangle with a height of 6.5 cm and a base of 20 cm.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \, \text{cm} \times 6.5 \, \text{cm} = 65 \, \text{cm}^2
\]

#### 8. Find the area of a trapezoid with a height of 4 cm and bases of 6 cm and 8 cm.
\[
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (6 \, \text{cm} + 8 \, \text{cm}) \times 4 \, \text{cm} = \frac{1}{2} \times 14 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2
\]

#### 9. Find the area of a rhombus with a base of 5 ft and a height of 85 ft.
\[
\text{Area} = \text{base} \times \text{height} = 5 \, \text{ft} \times 85 \, \text{ft} = 425 \, \text{ft}^2
\]

#### 10. Find the area of a rectangle with dimensions 6 yd and 8 yd.
\[
\text{Area} = \text{length} \times \text{width} = 6 \, \text{yd} \times 8 \, \text{yd} = 48 \, \text{yd}^2
\]

#### 11. Find the area of a triangle with a base of 30 cm and a height of 30 cm.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 30 \, \text{cm} \times 30 \, \text{cm} = 450 \, \text{cm}^2
\]

#### 12. Find the area of a trapezoid with a height of 30 m and bases of 30 m and 50 m.
\[
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (30 \, \text{m} + 50 \, \text{m}) \times 30 \, \text{m} = \frac{1}{2} \times 80 \, \text{m} \times 30 \, \text{m} = 1200 \, \text{m}^2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 15 \, \text{cm}^2 \\
2. & 9 \, \text{m}^2 \\
3. & 990 \, \text{in}^2 \\
4. & 6 \, \text{cm}^2 \\
5. & 12 \, \text{m}^2 \\
6. & 56 \, \text{cm}^2 \\
7. & 65 \, \text{cm}^2 \\
8. & 28 \, \text{cm}^2 \\
9. & 425 \, \text{ft}^2 \\
10. & 48 \, \text{yd}^2 \\
11. & 450 \, \text{cm}^2 \\
12. & 1200 \, \text{m}^2 \\
\end{array}
}
\]