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:
Area of a 12 cm by 5 cm rectangle is 34 cm.
Corrected: Area of a 12 cm by 5 cm rectangle is 60 sq cm.
12 x 5 = 60 sq cm; 34 is the perimeter formula 2(12+5), not the area.
2. Fix the sentence:
A 10 m by 10 m square has perimeter 100 m.
Corrected: A 10 m by 10 m square has perimeter 40 m.
Perimeter = 4 x 10 = 40 m; 100 is the area in square meters of the same square.
3. Fix the sentence:
A rectangle 7 ft by 2 ft has area 14 ft.
Corrected: A rectangle 7 ft by 2 ft has area 14 sq ft.
The number 14 is correct, but area must be labeled in square feet, not regular feet.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A 15 cm by 6 cm rectangle has area 90 sq cm.
A = 15 x 6 = 90 square centimeters using the rectangle area formula.
2. A 12 m by 8 m rectangle has perimeter 40 m.
P = 2(12+8) = 2 x 20 = 40 meters using the perimeter formula.
3. A square with side 9 ft has area 81 sq ft.
Area of a square = side x side = 9 x 9 = 81 square feet.
4. A rectangle 11 in by 4 in has perimeter 30 in.
P = 2(11+4) = 2 x 15 = 30 inches around the rectangle.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why must area be measured in square units like sq ft?
Sample answer: Area covers a two-dimensional surface, so we count square units that fit inside. Multiplying two lengths in feet produces square feet, which describes how much surface is covered.
Multiplying feet by feet gives square feet, which represents two-dimensional coverage rather than one-dimensional length.
2. A rug is 9 ft by 6 ft. How much trim and how much carpet do you need?
Sample answer: Trim equals perimeter: 2(9+6) = 30 ft. Carpet equals area: 9 x 6 = 54 sq ft. So you buy 30 feet of trim and 54 square feet of carpet.
Perimeter measures border length for trim, while area measures inside coverage for carpet, each with proper units.