Find the area and perimeter of the following rectangular shapes.
Geometry worksheet with eight rectangular shapes, each labeled with dimensions in yards, inches, and feet, asking students to find the area and perimeter.
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Step-by-step solution for: Area and perimeter of rectangles worksheets - Math Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Area and perimeter of rectangles worksheets - Math Worksheets ...
To solve the problem of finding the area and perimeter of the given rectangular shapes, we will use the following formulas:
1. Area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]
2. Perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]
#### Rectangle 1:
- Dimensions: Length = 31 yd, Width = 6 yd
- Area:
\[
\text{Area} = 31 \, \text{yd} \times 6 \, \text{yd} = 186 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (31 \, \text{yd} + 6 \, \text{yd}) = 2 \times 37 \, \text{yd} = 74 \, \text{yd}
\]
#### Rectangle 2:
- Dimensions: Length = 22 in, Width = 19 in
- Area:
\[
\text{Area} = 22 \, \text{in} \times 19 \, \text{in} = 418 \, \text{in}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (22 \, \text{in} + 19 \, \text{in}) = 2 \times 41 \, \text{in} = 82 \, \text{in}
\]
#### Rectangle 3:
- Dimensions: Length = 24 in, Width = 23 in
- Area:
\[
\text{Area} = 24 \, \text{in} \times 23 \, \text{in} = 552 \, \text{in}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (24 \, \text{in} + 23 \, \text{in}) = 2 \times 47 \, \text{in} = 94 \, \text{in}
\]
#### Rectangle 4:
- Dimensions: Length = 24 ft, Width = 17 ft
- Area:
\[
\text{Area} = 24 \, \text{ft} \times 17 \, \text{ft} = 408 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (24 \, \text{ft} + 17 \, \text{ft}) = 2 \times 41 \, \text{ft} = 82 \, \text{ft}
\]
#### Rectangle 5:
- Dimensions: Length = 30 ft, Width = 16 ft
- Area:
\[
\text{Area} = 30 \, \text{ft} \times 16 \, \text{ft} = 480 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (30 \, \text{ft} + 16 \, \text{ft}) = 2 \times 46 \, \text{ft} = 92 \, \text{ft}
\]
#### Rectangle 6:
- Dimensions: Length = 25 yd, Width = 13 yd
- Area:
\[
\text{Area} = 25 \, \text{yd} \times 13 \, \text{yd} = 325 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (25 \, \text{yd} + 13 \, \text{yd}) = 2 \times 38 \, \text{yd} = 76 \, \text{yd}
\]
#### Rectangle 7:
- Dimensions: Length = 31 yd, Width = 12 yd
- Area:
\[
\text{Area} = 31 \, \text{yd} \times 12 \, \text{yd} = 372 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (31 \, \text{yd} + 12 \, \text{yd}) = 2 \times 43 \, \text{yd} = 86 \, \text{yd}
\]
#### Rectangle 8:
- Dimensions: Length = 18 ft, Width = 12 ft
- Area:
\[
\text{Area} = 18 \, \text{ft} \times 12 \, \text{ft} = 216 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (18 \, \text{ft} + 12 \, \text{ft}) = 2 \times 30 \, \text{ft} = 60 \, \text{ft}
\]
\[
\boxed{
\begin{array}{ll}
\text{Rectangle 1:} & \text{Area} = 186 \, \text{yd}^2, \, \text{Perimeter} = 74 \, \text{yd} \\
\text{Rectangle 2:} & \text{Area} = 418 \, \text{in}^2, \, \text{Perimeter} = 82 \, \text{in} \\
\text{Rectangle 3:} & \text{Area} = 552 \, \text{in}^2, \, \text{Perimeter} = 94 \, \text{in} \\
\text{Rectangle 4:} & \text{Area} = 408 \, \text{ft}^2, \, \text{Perimeter} = 82 \, \text{ft} \\
\text{Rectangle 5:} & \text{Area} = 480 \, \text{ft}^2, \, \text{Perimeter} = 92 \, \text{ft} \\
\text{Rectangle 6:} & \text{Area} = 325 \, \text{yd}^2, \, \text{Perimeter} = 76 \, \text{yd} \\
\text{Rectangle 7:} & \text{Area} = 372 \, \text{yd}^2, \, \text{Perimeter} = 86 \, \text{yd} \\
\text{Rectangle 8:} & \text{Area} = 216 \, \text{ft}^2, \, \text{Perimeter} = 60 \, \text{ft} \\
\end{array}
}
\]
Formulas:
1. Area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]
2. Perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]
Step-by-Step Solution:
#### Rectangle 1:
- Dimensions: Length = 31 yd, Width = 6 yd
- Area:
\[
\text{Area} = 31 \, \text{yd} \times 6 \, \text{yd} = 186 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (31 \, \text{yd} + 6 \, \text{yd}) = 2 \times 37 \, \text{yd} = 74 \, \text{yd}
\]
#### Rectangle 2:
- Dimensions: Length = 22 in, Width = 19 in
- Area:
\[
\text{Area} = 22 \, \text{in} \times 19 \, \text{in} = 418 \, \text{in}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (22 \, \text{in} + 19 \, \text{in}) = 2 \times 41 \, \text{in} = 82 \, \text{in}
\]
#### Rectangle 3:
- Dimensions: Length = 24 in, Width = 23 in
- Area:
\[
\text{Area} = 24 \, \text{in} \times 23 \, \text{in} = 552 \, \text{in}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (24 \, \text{in} + 23 \, \text{in}) = 2 \times 47 \, \text{in} = 94 \, \text{in}
\]
#### Rectangle 4:
- Dimensions: Length = 24 ft, Width = 17 ft
- Area:
\[
\text{Area} = 24 \, \text{ft} \times 17 \, \text{ft} = 408 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (24 \, \text{ft} + 17 \, \text{ft}) = 2 \times 41 \, \text{ft} = 82 \, \text{ft}
\]
#### Rectangle 5:
- Dimensions: Length = 30 ft, Width = 16 ft
- Area:
\[
\text{Area} = 30 \, \text{ft} \times 16 \, \text{ft} = 480 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (30 \, \text{ft} + 16 \, \text{ft}) = 2 \times 46 \, \text{ft} = 92 \, \text{ft}
\]
#### Rectangle 6:
- Dimensions: Length = 25 yd, Width = 13 yd
- Area:
\[
\text{Area} = 25 \, \text{yd} \times 13 \, \text{yd} = 325 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (25 \, \text{yd} + 13 \, \text{yd}) = 2 \times 38 \, \text{yd} = 76 \, \text{yd}
\]
#### Rectangle 7:
- Dimensions: Length = 31 yd, Width = 12 yd
- Area:
\[
\text{Area} = 31 \, \text{yd} \times 12 \, \text{yd} = 372 \, \text{yd}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (31 \, \text{yd} + 12 \, \text{yd}) = 2 \times 43 \, \text{yd} = 86 \, \text{yd}
\]
#### Rectangle 8:
- Dimensions: Length = 18 ft, Width = 12 ft
- Area:
\[
\text{Area} = 18 \, \text{ft} \times 12 \, \text{ft} = 216 \, \text{ft}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (18 \, \text{ft} + 12 \, \text{ft}) = 2 \times 30 \, \text{ft} = 60 \, \text{ft}
\]
Final Answers:
\[
\boxed{
\begin{array}{ll}
\text{Rectangle 1:} & \text{Area} = 186 \, \text{yd}^2, \, \text{Perimeter} = 74 \, \text{yd} \\
\text{Rectangle 2:} & \text{Area} = 418 \, \text{in}^2, \, \text{Perimeter} = 82 \, \text{in} \\
\text{Rectangle 3:} & \text{Area} = 552 \, \text{in}^2, \, \text{Perimeter} = 94 \, \text{in} \\
\text{Rectangle 4:} & \text{Area} = 408 \, \text{ft}^2, \, \text{Perimeter} = 82 \, \text{ft} \\
\text{Rectangle 5:} & \text{Area} = 480 \, \text{ft}^2, \, \text{Perimeter} = 92 \, \text{ft} \\
\text{Rectangle 6:} & \text{Area} = 325 \, \text{yd}^2, \, \text{Perimeter} = 76 \, \text{yd} \\
\text{Rectangle 7:} & \text{Area} = 372 \, \text{yd}^2, \, \text{Perimeter} = 86 \, \text{yd} \\
\text{Rectangle 8:} & \text{Area} = 216 \, \text{ft}^2, \, \text{Perimeter} = 60 \, \text{ft} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of find the area of a rectangle worksheet.