Area and Perimeter

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Answer Key & Explanations

Area and Perimeter · Grade 4 · Worksheet 3

1. Liam is building a rectangular garden bed that is 12 feet long and 8 feet wide. He wants to put a fence around the entire garden and also cover the entire area with soil. How many feet of fencing does Liam 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: Identify the given dimensions of the rectangular garden bed. Length = 12 feet Width = 8 feet Calculate the perimeter (fencing needed).
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Identify the given dimensions of the rectangular garden bed.** Length = 12 feet Width = 8 feet --- **Step 2: Calculate the perimeter (fencing needed).** The formula for the perimeter \( P \) of a rectangle is: P = 2 × (Length + Width) Substitute the values: P = 2 × (12 + 8) P = 2 × 20 P = 40 feet So, Liam needs **40 feet of fencing**. --- **Step 3: Calculate the area (soil needed).** The formula for the area \( A \) of a rectangle is: A = Length × Width Substitute the values: A = 12 × 8 A = 96 square feet So, Liam needs **96 square feet of soil**. --- **Final Answer:** Perimeter: 40 feet, Area: 96 square feet

2. Maria is designing a rectangular banner for the school science fair. The banner needs to be 15 feet long and 6 feet wide. She wants to outline the entire banner with colorful ribbon and also cover the entire surface with special science-themed fabric. How many feet of ribbon does she need for the perimeter, and how many square feet of fabric does she need to cover the area? Answer: 42 feet of ribbon and 90 square feet of fabric Solution: Find the perimeter for the ribbon. The formula for perimeter of a rectangle is P = 2 × (length + width). Calculate perimeter: P = 2 × (15 + 6) = 2 × 21 = 42 feet.
   Full step-by-step solution

   Step 1: Find the perimeter for the ribbon. The formula for perimeter of a rectangle is P = 2 × (length + width). Step 2: Calculate perimeter: P = 2 × (15 + 6) = 2 × 21 = 42 feet. Step 3: Find the area for the fabric. The formula for area of a rectangle is A = length × width. Step 4: Calculate area: A = 15 × 6 = 90 square feet. Step 5: Maria needs 42 feet of ribbon for the perimeter and 90 square feet of fabric for the area.

3. Oliver is planting a rectangular vegetable garden that is 6 meters long and 9 meters wide. Oliver wants to know the area of the garden to buy enough soil. What is the area? Answer: 54 Solution: The area of a rectangle is length × width. Length = 6 meters, width = 9 meters. Multiply: 6 × 9 = 54.
   Full step-by-step solution

   Step 1: The area of a rectangle is length × width. Step 2: Length = 6 meters, width = 9 meters. Step 3: Multiply: 6 × 9 = 54. The answer is 54 square meters.