Area and Perimeter (Advanced) — Answer Key
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
6 x 6 = 36 square ft beats 32, 20, and 11; the square shape maximizes area for a given perimeter.
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
8 x 4 = 32 square ft, smaller than the 36 square ft maximum from a 6 by 6 garden.
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
11 x 1 equals 11 square ft, showing how skinny rectangles waste planting space.
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.
Among rectangles with the same perimeter, equal length and width maximize the product, so a square wins.
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.
24 divided by 4 equals 6, the side length of the square that maximizes the rectangular area.
2. A 6 ft by 6 ft garden has an area of 36 square ft.
6 x 6 = 36 square ft, the largest possible area within a 24 ft perimeter.
3. A 7 ft by 5 ft rectangle uses 24 ft of fence and has an area of 35 square ft.
7 x 5 = 35 square ft, just below the 36 square ft maximum, showing how close to square works best.
4. The closer a rectangle's dimensions are to equal, the larger its area for a fixed perimeter.
Equal dimensions form a square, which maximizes area among all rectangles with the same perimeter.
5. Area is reported in square ft because it covers a two-dimensional surface.
Multiplying ft by ft gives square ft, the proper Grade 4 unit for rectangular garden area.