Worksheet On Area Of Square And Rectangle

Mastering Area: A Comprehensive Worksheet on Squares and Rectangles

Understanding the area of squares and rectangles is fundamental to geometry and numerous real-world applications. This worksheet provides a structured approach to mastering this concept, progressing from basic calculations to more challenging problems involving word problems and composite shapes. We'll cover the formulas, provide numerous examples, and offer solutions to help you solidify your understanding. Let's begin!

Understanding Area: The Basics

Before diving into calculations, let's define what area means. The area of a two-dimensional shape is the amount of space it occupies. Think of it as the space inside the shape's boundaries. We measure area in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).

Squares: Sides and Area

A square is a quadrilateral with four equal sides and four right angles (90° angles). To calculate the area of a square, you simply multiply the length of one side by itself. This is because all sides are equal.

Formula for the Area of a Square:

Area = side × side = side²

Example:

A square has a side length of 5 cm. What is its area?

Area = 5 cm × 5 cm = 25 cm²

Rectangles: Length, Width, and Area

A rectangle is a quadrilateral with four right angles and opposite sides that are equal in length. Unlike a square, a rectangle's length and width can be different. To find the area of a rectangle, you multiply its length by its width.

Formula for the Area of a Rectangle:

Area = length × width

Example:

A rectangle has a length of 8 meters and a width of 3 meters. What is its area?

Area = 8 m × 3 m = 24 m²

Practice Problems: Squares

Let's start with some practice problems focusing on squares. Remember to always include the units in your answer!

Problem 1:

Find the area of a square with a side length of 12 inches.

Problem 2:

A square garden has an area of 64 square feet. What is the length of one side of the garden?

Problem 3:

A square tile has a side length of 10 centimeters. If you need to cover a floor with an area of 1000 square centimeters, how many tiles will you need?

Practice Problems: Rectangles

Now let's tackle some problems involving rectangles. Remember the formula: Area = length × width.

Problem 4:

Calculate the area of a rectangle with a length of 15 cm and a width of 7 cm.

Problem 5:

A rectangular room measures 12 feet in length and 9 feet in width. What is the area of the room?

Problem 6:

A rectangular piece of fabric has an area of 72 square inches. If the length is 9 inches, what is the width?

Word Problems: Putting It All Together

Real-world problems often require you to apply your knowledge of area to different scenarios. Let's try some word problems that combine the concepts of squares and rectangles.

Problem 7:

A farmer wants to fence a rectangular field that measures 20 meters by 30 meters. What is the area of the field? If fencing costs $5 per meter, how much will it cost to fence the entire field? (Hint: Remember to consider all four sides of the rectangle for the fencing cost).

Problem 8:

A square carpet has a side length of 4 meters. What is the area of the carpet? If a rectangular room measures 5 meters by 6 meters, will the carpet cover the entire floor? If not, what is the uncovered area?

Problem 9:

A rectangular swimming pool is 15 feet long and 10 feet wide. A square patio surrounds the pool with a width of 2 feet on all sides. What is the total area of the pool and patio combined?

Composite Shapes: Combining Squares and Rectangles

Sometimes you'll encounter shapes that are a combination of squares and rectangles. To find the total area of these composite shapes, you need to break them down into simpler shapes, calculate the area of each part, and then add the areas together.

Problem 10:

Imagine an "L" shaped figure. The larger rectangle measures 8 cm by 5 cm. The smaller rectangle, which forms the "L" shape, measures 3 cm by 2 cm. What is the total area of the "L" shaped figure?

Problem 11:

Consider a figure made of a square with a side length of 6 meters and a rectangle attached to one side, measuring 6 meters by 4 meters. Find the total area of this composite figure.

Problem 12: A playground is shaped like a large rectangle with a smaller square cut out of one corner. The rectangle is 25 meters by 20 meters, and the square is 5 meters by 5 meters. What is the total area of the playground?

Advanced Problems: Challenging Your Skills

These problems will push your understanding of area to a higher level.

Problem 13: A rectangular garden is twice as long as it is wide. If the area of the garden is 50 square meters, what are the dimensions (length and width) of the garden?

Problem 14: A square painting is surrounded by a frame that is 2 inches wide. If the area of the painting is 100 square inches, what is the total area of the painting and the frame combined?

Problem 15: A farmer has a rectangular field that measures 100 meters by 50 meters. He wants to divide the field into four equal smaller rectangular plots. What is the area of each smaller plot?

Solutions to Practice Problems

This section provides the answers to the practice problems, allowing you to check your work and identify any areas where you need further review. Remember to go back and try to solve the problems yourself before checking the answers.

Problem 1 Solution: 144 square inches (12 in × 12 in)

Problem 2 Solution: 8 feet (√64 ft²)

Problem 3 Solution: 100 tiles (1000 cm² / 100 cm² per tile)

Problem 4 Solution: 105 cm² (15 cm × 7 cm)

Problem 5 Solution: 108 ft² (12 ft × 9 ft)

Problem 6 Solution: 8 inches (72 in² / 9 in)

Problem 7 Solution: Area of field: 600 m²; Fencing cost: $200 ($5/meter × 100 meters perimeter)

Problem 8 Solution: Carpet area: 16 m²; No, the carpet will not cover the entire floor. Uncovered area: 14 m² (30 m² - 16 m²)

Problem 9 Solution: Pool area: 150 ft²; Patio area: 150 ft² ; Total area: 300 ft² (15 ft x 10 ft + (19 ft x 14 ft) - (15 ft x 10 ft) )

Problem 10 Solution: 34 cm² (40 cm² - 6 cm²)

Problem 11 Solution: 60 m² (36 m² + 24 m²)

Problem 12 Solution: 475 m² (500 m² - 25 m²)

Problem 13 Solution: Width: 5 meters; Length: 10 meters

Problem 14 Solution: 164 square inches (100 sq in + 64 sq in)

Problem 15 Solution: 1250 m² (5000 m² / 4)

This comprehensive worksheet provides a strong foundation in calculating the area of squares and rectangles. Remember, consistent practice is key to mastering these concepts. Use this worksheet as a tool to build your skills and confidently tackle more complex geometry problems. Good luck!