Question 1
Area of a Rectangle
A rectangular playground has a length of 9 meters and a width of 4 meters.
What is the area of the playground? square meters.
Solution: Area = length × width = 9 × 4 = 36 square meters.
4th Grade Math Diagnostic Test — Units 13–14
Area, Perimeter, Measurement Units & Elapsed Time. Limit: 60 Minutes.
Question 2
Perimeter of a Rectangle
The same playground has a length of 9 meters and a width of 4 meters.
What is the perimeter of the playground? meters.
Solution: Perimeter = 2 × (length + width) = 2 × (9 + 4) = 2 × 13 = 26 meters.
Question 3
Finding Unknown Side from Area
A rectangular rug has an area of 56 square feet. Its length is 8 feet.
What is its width? feet.
Solution: Width = Area ÷ Length = 56 ÷ 8 = 7 feet.
Question 4
Finding Unknown Side from Perimeter
A rectangular picture frame has a total perimeter of 28 cm. Its length is 9 cm.
What is its width? cm.
Solution: Half perimeter = 28 ÷ 2 = 14 cm. Width = 14 − 9 = 5 cm. (Check: 9 + 5 + 9 + 5 = 28 cm).
Question 5
Area of a Square
A square sandbox has a side length of 7 inches.
What is the area of the sandbox? square inches.
Solution: Area = side × side = 7 × 7 = 49 square inches.
Question 6
Perimeter vs. Area Concept
A garden is 12 feet long and 6 feet wide. Which measurement determines how much fencing is needed to surround the outside boundary of the garden?
Solution: Fencing goes around the outside border, so it measures Perimeter = 2(12 + 6) = 36 feet.
Question 7
Covering Surface Area
How many square feet of grass sod are needed to completely cover the interior of the 12-ft by 6-ft garden?
square feet.
Solution: Covering space inside requires Area = 12 × 6 = 72 square feet.
Question 8
Composite Rectilinear Area
An L-shaped hallway is split into two non-overlapping rectangular sections: Section A is 6m by 4m, and Section B is 3m by 2m.
What is the total area of the hallway? square meters.
Solution: Area A = 6 × 4 = 24. Area B = 3 × 2 = 6. Total = 24 + 6 = 30 square meters.
Question 9
Customary Length: Feet to Inches
Convert 4 feet into inches (1 foot = 12 inches):
4 feet = inches.
Solution: 4 × 12 = 48 inches.
Question 10
Customary Length: Yards to Feet
Convert 6 yards into feet (1 yard = 3 feet):
6 yards = feet.
Solution: 6 × 3 = 18 feet.
Question 11
Customary Weight: Pounds to Ounces
Convert 3 pounds into ounces (1 pound = 16 ounces):
3 pounds = ounces.
Solution: 3 × 16 = 48 ounces.
Question 12
Liquid Volume: Gallons to Quarts
How many quarts are in 3 gallons? (1 gallon = 4 quarts)
Solution: 3 gallons × 4 quarts per gallon = 12 quarts.
Question 13
Metric Length: Meters to Centimeters
Convert 7 meters into centimeters (1 meter = 100 cm):
7 meters = centimeters.
Solution: 7 × 100 = 700 centimeters.
Question 14
Metric Mass: Kilograms to Grams
Convert 5 kilograms into grams (1 kilogram = 1,000 grams):
5 kilograms = grams.
Solution: 5 × 1,000 = 5,000 grams.
Question 15
Time: Hours to Minutes
Convert 4 hours into minutes (1 hour = 60 minutes):
4 hours = minutes.
Solution: 4 × 60 = 240 minutes.
Question 16
Elapsed Time Word Problem
Soccer practice began at 3:20 PM and ended at 5:05 PM.
What was the total duration of practice in minutes? minutes.
Solution: 3:20 to 5:05 is 1 hour and 45 minutes. (1 × 60) + 45 = 105 minutes.