Math worksheet for calculating area and perimeter of quadrilaterals.

To solve the problem, we need to identify each quadrilateral, calculate its area and perimeter, and determine its type. Let's go through each shape step by step.

1) Trapezoid

- Type: Trapezoid
- Given:
- \( a1 = 8.7 \, \text{ft} \)
- \( a2 = 4.1 \, \text{ft} \)
- \( b1 = 5.86 \, \text{ft} \)
- \( b2 = 4.23 \, \text{ft} \)
- \( h = 4.2 \, \text{ft} \)

#### Area:
The formula for the area of a trapezoid is:
\[
\text{Area} = \frac{1}{2} \times (a1 + a2) \times h
\]
\[
\text{Area} = \frac{1}{2} \times (8.7 + 4.1) \times 4.2
\]
\[
\text{Area} = \frac{1}{2} \times 12.8 \times 4.2
\]
\[
\text{Area} = 6.4 \times 4.2 = 26.88 \, \text{ft}^2
\]

#### Perimeter:
The perimeter is the sum of all sides:
\[
\text{Perimeter} = a1 + a2 + b1 + b2
\]
\[
\text{Perimeter} = 8.7 + 4.1 + 5.86 + 4.23
\]
\[
\text{Perimeter} = 22.99 \, \text{ft}
\]

2) Parallelogram

- Type: Parallelogram
- Given:
- \( a = 4.38 \, \text{yds} \)
- \( c = 9.9 \, \text{yds} \)
- \( h = 4.1 \, \text{yds} \)

#### Area:
The formula for the area of a parallelogram is:
\[
\text{Area} = a \times h
\]
\[
\text{Area} = 4.38 \times 4.1
\]
\[
\text{Area} = 17.958 \, \text{yds}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 2 \times (a + c)
\]
\[
\text{Perimeter} = 2 \times (4.38 + 9.9)
\]
\[
\text{Perimeter} = 2 \times 14.28 = 28.56 \, \text{yds}
\]

3) Square

- Type: Square
- Given:
- \( s = 6.8 \, \text{mm} \)

#### Area:
The formula for the area of a square is:
\[
\text{Area} = s^2
\]
\[
\text{Area} = 6.8^2
\]
\[
\text{Area} = 46.24 \, \text{mm}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 4 \times s
\]
\[
\text{Perimeter} = 4 \times 6.8 = 27.2 \, \text{mm}
\]

4) Rhombus

- Type: Rhombus
- Given:
- \( a = 5.5 \, \text{inches} \)
- \( h = 5.02 \, \text{inches} \)

#### Area:
The formula for the area of a rhombus is:
\[
\text{Area} = a \times h
\]
\[
\text{Area} = 5.5 \times 5.02
\]
\[
\text{Area} = 27.61 \, \text{inches}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 4 \times a
\]
\[
\text{Perimeter} = 4 \times 5.5 = 22 \, \text{inches}
\]

5) Rectangle

- Type: Rectangle
- Given:
- \( a = 7.9 \, \text{inches} \)
- \( b = 4.8 \, \text{inches} \)

#### Area:
The formula for the area of a rectangle is:
\[
\text{Area} = a \times b
\]
\[
\text{Area} = 7.9 \times 4.8
\]
\[
\text{Area} = 37.92 \, \text{inches}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 2 \times (a + b)
\]
\[
\text{Perimeter} = 2 \times (7.9 + 4.8)
\]
\[
\text{Perimeter} = 2 \times 12.7 = 25.4 \, \text{inches}
\]

6) Parallelogram

- Type: Parallelogram
- Given:
- \( a = 4.42 \, \text{ft} \)
- \( c = 10 \, \text{ft} \)
- \( h = 4.2 \, \text{ft} \)

#### Area:
The formula for the area of a parallelogram is:
\[
\text{Area} = a \times h
\]
\[
\text{Area} = 4.42 \times 4.2
\]
\[
\text{Area} = 18.564 \, \text{ft}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 2 \times (a + c)
\]
\[
\text{Perimeter} = 2 \times (4.42 + 10)
\]
\[
\text{Perimeter} = 2 \times 14.42 = 28.84 \, \text{ft}
\]

7) Square

- Type: Square
- Given:
- \( s = 5.1 \, \text{yds} \)

#### Area:
The formula for the area of a square is:
\[
\text{Area} = s^2
\]
\[
\text{Area} = 5.1^2
\]
\[
\text{Area} = 26.01 \, \text{yds}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 4 \times s
\]
\[
\text{Perimeter} = 4 \times 5.1 = 20.4 \, \text{yds}
\]

8) Rectangle

- Type: Rectangle
- Given:
- \( a = 8.7 \, \text{cm} \)
- \( b = 4.6 \, \text{cm} \)

#### Area:
The formula for the area of a rectangle is:
\[
\text{Area} = a \times b
\]
\[
\text{Area} = 8.7 \times 4.6
\]
\[
\text{Area} = 40.02 \, \text{cm}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 2 \times (a + b)
\]
\[
\text{Perimeter} = 2 \times (8.7 + 4.6)
\]
\[
\text{Perimeter} = 2 \times 13.3 = 26.6 \, \text{cm}
\]

9) Rhombus

- Type: Rhombus
- Given:
- \( a = 5 \, \text{mm} \)
- \( h = 4.6 \, \text{mm} \)

#### Area:
The formula for the area of a rhombus is:
\[
\text{Area} = a \times h
\]
\[
\text{Area} = 5 \times 4.6
\]
\[
\text{Area} = 23 \, \text{mm}^2
\]

#### Perimeter:
The perimeter is:
\[
\text{Perimeter} = 4 \times a
\]
\[
\text{Perimeter} = 4 \times 5 = 20 \, \text{mm}
\]

Final Answers

\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Shape} & \text{Area} & \text{Perimeter} & \text{Type} \\
\hline
1) & 26.88 \, \text{ft}^2 & 22.99 \, \text{ft} & \text{Trapezoid} \\
2) & 17.958 \, \text{yds}^2 & 28.56 \, \text{yds} & \text{Parallelogram} \\
3) & 46.24 \, \text{mm}^2 & 27.2 \, \text{mm} & \text{Square} \\
4) & 27.61 \, \text{inches}^2 & 22 \, \text{inches} & \text{Rhombus} \\
5) & 37.92 \, \text{inches}^2 & 25.4 \, \text{inches} & \text{Rectangle} \\
6) & 18.564 \, \text{ft}^2 & 28.84 \, \text{ft} & \text{Parallelogram} \\
7) & 26.01 \, \text{yds}^2 & 20.4 \, \text{yds} & \text{Square} \\
8) & 40.02 \, \text{cm}^2 & 26.6 \, \text{cm} & \text{Rectangle} \\
9) & 23 \, \text{mm}^2 & 20 \, \text{mm} & \text{Rhombus} \\
\hline
\end{array}
}
\]