Area and Perimeter

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Answer Key & Explanations

Area and Perimeter · Grade 4 · Worksheet 1

1. A rectangular garden measures 12.5 meters long and 8.4 meters wide. What is the area of the garden in square meters? Answer: 105 Solution: To find the area of a rectangle, we use the formula: Area = length × width Write down the given measurements. Length = 12.5 meters Width = 8.4 meters Multiply length by width.
   Full step-by-step solution

   To find the area of a rectangle, we use the formula: Area = length × width Step 1: Write down the given measurements. Length = 12.5 meters Width = 8.4 meters Step 2: Multiply length by width. 12.5 × 8.4 Step 3: Break the multiplication into simpler parts. First, multiply 12.5 by 8: 12.5 × 8 = 100 Step 4: Multiply 12.5 by 0.4: 12.5 × 0.4 = 5 Step 5: Add the two results: 100 + 5 = 105 Step 6: Include the unit. Area = 105 square meters So, the area of the garden is 105 square meters.

2. Liam is building a rectangular garden bed that measures 12 feet long and 8 feet wide. He wants to put a wooden border around the entire garden and also cover the garden area with soil. How many feet of wooden border does he need for the perimeter, and how many square feet of soil does he need to cover the area? Answer: Perimeter: 40 feet, Area: 96 square feet Solution: - Length = 12 feet - Width = 8 feet 1. Wooden border for the perimeter (in feet) 2.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** We have a rectangular garden bed: - Length = 12 feet - Width = 8 feet We need: 1. Wooden border for the **perimeter** (in feet) 2. Soil to cover the **area** (in square feet) --- **Step 2: Find the perimeter** The formula for the perimeter of a rectangle is: Perimeter = 2 × (Length + Width) Substitute the given values: Perimeter = 2 × (12 + 8) Perimeter = 2 × (20) Perimeter = 40 feet So, the wooden border needed is **40 feet**. --- **Step 3: Find the area** The formula for the area of a rectangle is: Area = Length × Width Substitute the given values: Area = 12 × 8 Area = 96 square feet So, the soil needed is **96 square feet**. --- **Step 4: Final answer** Perimeter: 40 feet Area: 96 square feet

3. Sam is tiling a rectangular bathroom wall. The wall is 3 feet long and 13 feet wide. What is the area of the wall in square feet? Answer: 39 Solution: Identify the length (3 feet) and the width (13 feet). Multiply length by width to find the area: 3 × 13 = 39. The area of the wall is 39 square feet.
   Full step-by-step solution

   Step 1: Identify the length (3 feet) and the width (13 feet). Step 2: Multiply length by width to find the area: 3 × 13 = 39. The area of the wall is 39 square feet.

4. A rectangular swimming pool is drawn on a grid where each square represents 1 meter. The pool's longer side measures 15 meters and its shorter side measures 12 meters. What is the total area of the swimming pool in square meters? Answer: 180 Solution: Identify the length and width of the rectangle. The longer side is the length, which is 15 meters. The shorter side is the width, which is 12 meters.
   Full step-by-step solution

   Step 1: Identify the length and width of the rectangle. The longer side is the length, which is 15 meters. The shorter side is the width, which is 12 meters. Step 2: Recall the formula for the area of a rectangle: Area = length × width. Step 3: Substitute the given values into the formula: Area = 15 × 12. Step 4: Perform the multiplication: 15 × 12 = 180. Step 5: Include the units: The area is 180 square meters. The answer is 180.