Area of Squares, Rectangles, and Parallelograms worksheet with labeled dimensions for calculating area.

To solve the problem of finding the area of each shape, we need to use the appropriate formulas for squares, rectangles, and parallelograms. Let's go through each shape step by step.

Formulas Needed:

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

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

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

---

Solutions:

#### 1) Rectangle (7 km × 5 km)
\[
\text{Area} = \text{length} \times \text{width} = 7 \, \text{km} \times 5 \, \text{km} = 35 \, \text{km}^2
\]

#### 2) Parallelogram (6 m base, 6 m height)
\[
\text{Area} = \text{base} \times \text{height} = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2
\]

#### 3) Square (7 in side)
\[
\text{Area} = \text{side}^2 = 7 \, \text{in} \times 7 \, \text{in} = 49 \, \text{in}^2
\]

#### 4) Rectangle (32.3 yd × 22 yd)
\[
\text{Area} = \text{length} \times \text{width} = 32.3 \, \text{yd} \times 22 \, \text{yd} = 710.6 \, \text{yd}^2
\]

#### 5) Rectangle (10 in × 8 in)
\[
\text{Area} = \text{length} \times \text{width} = 10 \, \text{in} \times 8 \, \text{in} = 80 \, \text{in}^2
\]

#### 6) Parallelogram (5.9 in base, 4 in height)
\[
\text{Area} = \text{base} \times \text{height} = 5.9 \, \text{in} \times 4 \, \text{in} = 23.6 \, \text{in}^2
\]

#### 7) Rhombus (14.9 ft diagonals)
For a rhombus, the area can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times d_1 \times d_2
\]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. Here, both diagonals are given as 14.9 ft.
\[
\text{Area} = \frac{1}{2} \times 14.9 \, \text{ft} \times 14.9 \, \text{ft} = \frac{1}{2} \times 222.01 \, \text{ft}^2 = 111.005 \, \text{ft}^2
\]

#### 8) Square (27 mi side)
\[
\text{Area} = \text{side}^2 = 27 \, \text{mi} \times 27 \, \text{mi} = 729 \, \text{mi}^2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 35 \, \text{km}^2 \\
2) & 36 \, \text{m}^2 \\
3) & 49 \, \text{in}^2 \\
4) & 710.6 \, \text{yd}^2 \\
5) & 80 \, \text{in}^2 \\
6) & 23.6 \, \text{in}^2 \\
7) & 111.005 \, \text{ft}^2 \\
8) & 729 \, \text{mi}^2 \\
\end{array}
}
\]