Perimeter, Area, and Surface Area — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A 6 ft by 4 ft rectangle has area 20 ft.
Corrected: A 6 ft by 4 ft rectangle has area 24 sq ft.
Multiply 6 x 4 to get 24, and area is measured in square feet, not feet.
2. Fix the sentence:
Perimeter of a 5 m by 3 m rectangle is 15 m.
Corrected: Perimeter of a 5 m by 3 m rectangle is 16 m.
Use P = 2(5+3) = 16 m, not 5 x 3 which gives area instead of perimeter.
3. Fix the sentence:
An 8 cm square has perimeter 64 cm.
Corrected: An 8 cm square has perimeter 32 cm.
Perimeter of a square is 4 x side, so 4 x 8 = 32 cm; 64 is the area instead.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The perimeter of a rectangle 7 ft long and 3 ft wide is 20 ft.
P = 2(7+3) = 2 x 10 = 20 ft using the perimeter formula.
2. The area of a rectangle 9 m by 4 m is 36 square meters.
A = l x w = 9 x 4 = 36, and area uses square meters as the unit.
3. A square with 6 cm sides has perimeter 24 cm.
Perimeter = 4 x 6 = 24 cm because squares have four equal sides.
4. A rectangle 10 in long and 5 in wide has area 50 sq in.
A = 10 x 5 = 50 square inches, the standard area formula for rectangles.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain the difference between perimeter and area in your own words.
Sample answer: Perimeter measures the distance around a shape, while area measures the space inside the shape. Perimeter uses single units like feet; area uses square units like square feet.
Perimeter is a length around the boundary, but area covers the surface inside, which is why their units differ.
2. A garden is 8 ft by 5 ft. Find both its perimeter and area.
Sample answer: Perimeter = 2(8+5) = 26 ft. Area = 8 x 5 = 40 sq ft. The garden has 26 feet of border and covers 40 square feet of ground.
Apply P = 2(l+w) for fencing length and A = l x w for ground space, with correct linear and square units.