Word Problems: Area & Perimeter
Learn
Area and perimeter are used in many real-life situations! The key is knowing when to use each one.
When to Use Perimeter
- Fence around a yard - measuring the border
- Frame around a picture - going around the edge
- Border on a rug - the outer edge
Formula: Perimeter = Add all sides (or for rectangles: 2 x length + 2 x width)
When to Use Area
- Carpet for a floor - covering the space inside
- Paint for a wall - filling the surface
- Grass for a lawn - the space inside the border
Formula: Area = length x width (for rectangles)
Examples
Perimeter Example:
"Mr. Jones wants to put a fence around his rectangular garden. The garden is 8 feet long and 5 feet wide. How much fencing does he need?"
Solution: Perimeter = 2(8) + 2(5) = 16 + 10 = 26 feet of fencing
Area Example:
"Lisa wants to cover her bedroom floor with carpet. Her room is 9 feet long and 7 feet wide. How many square feet of carpet does she need?"
Solution: Area = 9 x 7 = 63 square feet of carpet
Practice
1. A rectangular pool is 10 meters long and 6 meters wide. What is the perimeter of the pool?
A) 16 meters
B) 32 meters
C) 60 meters
D) 60 square meters
Answer
B) 32 meters - Perimeter = 2(10) + 2(6) = 20 + 12 = 32 meters.
2. A farmer wants to plant grass on a rectangular field that is 8 yards by 6 yards. How many square yards of grass does he need?
A) 14 square yards
B) 28 square yards
C) 48 square yards
D) 48 yards
Answer
C) 48 square yards - Area = 8 x 6 = 48 square yards.
3. Emma is putting ribbon around a picture frame. The frame is 12 inches long and 8 inches wide. How much ribbon does she need?
A) 20 inches
B) 40 inches
C) 96 inches
D) 96 square inches
Answer
B) 40 inches - Perimeter (ribbon around edge) = 2(12) + 2(8) = 24 + 16 = 40 inches.
4. A basketball court is 28 meters long and 15 meters wide. What is the area of the court?
A) 43 square meters
B) 86 square meters
C) 420 square meters
D) 420 meters
Answer
C) 420 square meters - Area = 28 x 15 = 420 square meters.
5. Jake has a square garden where each side is 7 feet. What is the perimeter?
A) 7 feet
B) 14 feet
C) 28 feet
D) 49 feet
Answer
C) 28 feet - A square has 4 equal sides. Perimeter = 4 x 7 = 28 feet.
6. Maria wants to tile her bathroom floor. The floor is 5 feet by 4 feet. How many square feet of tile does she need?
A) 9 square feet
B) 18 square feet
C) 20 square feet
D) 20 feet
Answer
C) 20 square feet - Area = 5 x 4 = 20 square feet.
7. A rectangular park has a perimeter of 100 meters. If the length is 30 meters, what is the width?
A) 10 meters
B) 20 meters
C) 40 meters
D) 70 meters
Answer
B) 20 meters - 100 = 2(30) + 2(w), so 100 = 60 + 2w, 40 = 2w, w = 20 meters.
8. Which measurement would you use for how much paint to buy for a wall?
A) Perimeter
B) Area
C) Length only
D) Width only
Answer
B) Area - Paint covers the surface (inside), which is area.
9. A square room has an area of 36 square feet. What is the length of one side?
A) 4 feet
B) 6 feet
C) 9 feet
D) 18 feet
Answer
B) 6 feet - 6 x 6 = 36, so each side is 6 feet.
10. A dog run is 9 yards long and 4 yards wide. How much fencing is needed to go around it?
A) 13 yards
B) 26 yards
C) 36 yards
D) 36 square yards
Answer
B) 26 yards - Perimeter = 2(9) + 2(4) = 18 + 8 = 26 yards.
Next Steps
- Practice identifying area vs. perimeter situations
- Measure rooms in your house and calculate area and perimeter
- Continue to Common Mistakes