Area and Perimeter

Grade 4 · geometry · 93 practice problems · read aloud

🔊 Listen to this explanation

Area and Perimeter: A Guide for 4th Graders

1. What Are Area and Perimeter? 🤔

Perimeter is the distance around a shape. Think of it as the fence you'd need to put around a yard.

Area is the amount of space inside a shape. Think of it as the grass or tiles you'd need to cover the yard's floor.

We use them for real-life tasks like figuring out how much wood to build a frame (perimeter) or how much paint to cover a wall (area).

2. How to Solve Problems: Step-by-Step

  1. Step 1: Identify the Shape. Is it a rectangle or a square?
  2. Step 2: Find the Perimeter. Add up the lengths of all the sides. For a rectangle: P = 2 × (length + width)
  3. Step 3: Find the Area. Multiply the length by the width. For a rectangle: A = length × width
  4. Step 4: Don't Forget Units! Perimeter is in units (like ft). Area is in square units (like ft²).

3. Visual Examples

Example 1: A Square

Square side = 5 cm

Perimeter: 5 + 5 + 5 + 5 = 20 cm or 4 × 5 = 20 cm

Area: 5 cm × 5 cm = 25 cm²

Example 2: A Rectangle

Length = 8 ft, Width = 3 ft

Perimeter: 2 × (8 + 3) = 2 × 11 = 22 ft

Area: 8 ft × 3 ft = 24 ft²

4. Common Mistakes to Avoid 🚫

Mixing up Area and Perimeter: Remember, perimeter is the outside (fence), area is the inside (carpet).

Forgetting to Label Units: Always write the unit (like cm) for perimeter and the square unit (like cm²) for area.

Adding Wrong Sides: On a rectangle, make sure you are adding the two different side lengths, not just one.

5. Tips & Tricks

Memory Aid: Perimeter starts with a 'P' like 'Police' who patrol around the outside. Area is the space at the center.

Rectangle Shortcut: For perimeter, just add the length and width, then double it!

Draw It! Always sketch the shape and label the sides. This helps you see what you're working with.

6. How to Practice

  • Measure Your World: Find the area and perimeter of your notebook, a book, or a tile on the floor.
  • Use Graph Paper: Draw rectangles and count the squares inside for area, and count the units around the edges for perimeter.
  • Play Online Games: Search for "area and perimeter games for 4th grade" for fun, interactive practice!

Practice problems

6 of the 93, worked through step by step — try them before opening the answer.

1 Rectangle: length 124 cm, width 86 cm. Find area.

Hint: Think about what area means—it's the space inside the rectangle. You need to multiply the two side lengths together. Remember to write the answer in square units.

Show the answer

Answer: 10664

  1. Identify the length and width. Length = 124 cm, Width = 86 cm.
  2. Use the formula for area of a rectangle: Area = length × width.
  3. Multiply: 124 × 86.
  4. Break it into parts: 124 × 80 = 9920, and 124 × 6 = 744.
  5. Add the parts: 9920 + 744 = 10664.
  6. The area is 10664 square centimeters.

The answer is 10664.

2 Rectangle: length 125 cm, width 48 cm. Find area.

Hint: Think about how area is different from perimeter. Area measures the space inside the rectangle, not the distance around it. What operation combines the length and width to find that space?

Show the answer

Answer: 6000

  1. Recall the formula for area of a rectangle: Area = length × width.
  2. Substitute the given values: length = 125 cm, width = 48 cm.
  3. Multiply: 125 × 48.
  4. Break it down: 125 × 40 = 5000, and 125 × 8 = 1000.
  5. Add the partial products: 5000 + 1000 = 6000.
  6. Include the correct units: square centimeters. The area is 6000 square centimeters.

3 Rectangle: length 121 cm, width 96 cm. Find area.

Hint: Think about which two numbers you need to multiply to find the space inside a rectangle.

Show the answer

Answer: 11616

  1. Recall the formula for area of a rectangle: Area = length × width.
  2. Substitute the given values: Area = 121 × 96.
  3. Multiply: 121 × 96 = 121 × (100 − 4) = 12100 − 484 = 11616.
  4. The area is 11616 square centimeters.

The answer is 11616.

4 Rectangle: length 150 cm, width 90 cm. Find area.

Hint: Think about how to find the space inside a rectangle by multiplying its two side lengths.

Show the answer

Answer: 13500

  1. Identify the length and width. Length = 150 cm, Width = 90 cm.
  2. Recall the formula for area of a rectangle: Area = length × width.
  3. Substitute the values: Area = 150 × 90.
  4. Multiply: 150 × 90 = 150 × 9 × 10 = 1350 × 10 = 13500.
  5. The area is 13500 square centimeters.

The answer is 13500.

5 Rectangle: length 112 cm, width 85 cm. Find area.

Hint: Think about which two measurements you multiply together to find the space inside a rectangle.

Show the answer

Answer: 9520

  1. Recall the formula for area of a rectangle: Area = length × width.
  2. Substitute the given values: length = 112 cm, width = 85 cm.
  3. Multiply: 112 × 85.
  4. Break it down: 112 × 80 = 8960, and 112 × 5 = 560.
  5. Add the partial products: 8960 + 560 = 9520.
  6. The area is 9520 square centimeters.

The answer is 9520.

6 Rectangle: length 121 cm, width 76 cm. Find area.

Hint: Think about the formula that uses the two side lengths to find the space inside a rectangle.

Show the answer

Answer: 9196

  1. Recall the formula for area of a rectangle: Area = length × width.
  2. Substitute the given values: length = 121 cm, width = 76 cm.
  3. Multiply: 121 × 76.
  4. Break it down: 121 × 70 = 8470, and 121 × 6 = 726.
  5. Add the partial products: 8470 + 726 = 9196.
  6. The area is 9196 square centimeters.

The answer is 9196.

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