In this Grade 4 design challenge, students use a fixed 24 ft fence perimeter to find rectangular garden dimensions that maximize area. They compare 6 by 6, 8 by 4, 10 by 2, and 11 by 1 layouts, learning that a square produces the largest area of 36 square ft. Multiple choice and fill-in items reinforce that equal dimensions maximize area, building Grade 4 reasoning about optimization in real-world rectangular planning.
Style:
Area and Perimeter (Advanced)
Part A: Multiple Choice
Circle the best answer for each question.
1. A rectangular garden has a fixed perimeter of 24 ft. Which dimensions maximize its area?
A) 6 ft by 6 ft
B) 8 ft by 4 ft
C) 10 ft by 2 ft
D) 11 ft by 1 ft
2. What is the area of an 8 ft by 4 ft garden built with a 24 ft fence?
A) 32 square ft
B) 24 square ft
C) 36 square ft
D) 48 square ft
3. If you stretch the garden to 11 ft by 1 ft, the perimeter is still 24 ft. What is the area?
A) 11 square ft
B) 22 square ft
C) 12 square ft
D) 24 square ft
4. Why does a 6 ft by 6 ft square give the maximum area for a 24 ft fence?
A) Equal dimensions create the largest rectangular area for a fixed perimeter.
B) Squares always have a smaller area than long rectangles.
C) Perimeter and area are always equal for squares.
D) Multiplying by 1 always gives the largest answer.
Part B: Fill in the Blank
Write the correct answer on each line.
1. To maximize area with a 24 ft fence, choose a square garden with side 6 ft.
2. A 6 ft by 6 ft garden has an area of 36 square ft.
3. A 7 ft by 5 ft rectangle uses 24 ft of fence and has an area of 35 square ft.
4. The closer a rectangle's dimensions are to equal, the larger its area for a fixed perimeter.
5. Area is reported in square ft because it covers a two-dimensional surface.
Area and Perimeter (Advanced)
★ Part A: Multiple Choice
Circle the best answer for each question.
1. A rectangular garden has a fixed perimeter of 24 ft. Which dimensions maximize its area?
A) 6 ft by 6 ft
B) 8 ft by 4 ft
C) 10 ft by 2 ft
D) 11 ft by 1 ft
2. What is the area of an 8 ft by 4 ft garden built with a 24 ft fence?
A) 32 square ft
B) 24 square ft
C) 36 square ft
D) 48 square ft
3. If you stretch the garden to 11 ft by 1 ft, the perimeter is still 24 ft. What is the area?
A) 11 square ft
B) 22 square ft
C) 12 square ft
D) 24 square ft
4. Why does a 6 ft by 6 ft square give the maximum area for a 24 ft fence?
A) Equal dimensions create the largest rectangular area for a fixed perimeter.
B) Squares always have a smaller area than long rectangles.
C) Perimeter and area are always equal for squares.
D) Multiplying by 1 always gives the largest answer.
★ Part B: Fill in the Blank
Write the correct answer on each line.
1) To maximize area with a 24 ft fence, choose a square garden with side 6 ft.
2) A 6 ft by 6 ft garden has an area of 36 square ft.
3) A 7 ft by 5 ft rectangle uses 24 ft of fence and has an area of 35 square ft.
4) The closer a rectangle's dimensions are to equal, the larger its area for a fixed perimeter.
5) Area is reported in square ft because it covers a two-dimensional surface.
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9 Questions
12-18 minutes
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