This grade 4 area worksheet answer key solves all 22 problems of the area and perimeter of rectangles worksheet step by step.
This answer key gives a full worked solution for all 22 area and perimeter problems. Compare each step with your own work, and remember that area uses square units while perimeter uses plain units.
Grade 4 Area Worksheet Answer Key: problems 1–5
Problem 1: Count unit squares
There are 3 rows with 5 squares in each row. Counting the squares gives 15, and \(3 \times 5 = 15\).
15 square units
Problem 2: Area of rectangles
- \(4 \times 6 = 24\) square feet
- \(7 \times 3 = 21\) square inches
- \(9 \times 5 = 45\) square meters
- \(12 \times 8 = 96\) square yards
24 sq ft; 21 sq in; 45 sq m; 96 sq yd
Problem 3: Perimeter of rectangles
- \(2 \times 5 + 2 \times 3 = 10 + 6 = 16\) cm
- \(2 \times 8 + 2 \times 2 = 16 + 4 = 20\) cm
- \(2 \times 10 + 2 \times 6 = 20 + 12 = 32\) cm
- \(2 \times 15 + 2 \times 9 = 30 + 18 = 48\) cm
16 cm; 20 cm; 32 cm; 48 cm
Problem 4: Add the four sides
\(7 + 4 + 7 + 4 = 22\).
22 cm
Problem 5: Squares
- Area: \(6 \times 6 = 36\) sq in. Perimeter: \(4 \times 6 = 24\) in.
- Area: \(9 \times 9 = 81\) sq ft. Perimeter: \(4 \times 9 = 36\) ft.
- Area: \(12 \times 12 = 144\) sq m. Perimeter: \(4 \times 12 = 48\) m.
36 sq in and 24 in; 81 sq ft and 36 ft; 144 sq m and 48 m
Grade 4 Area Worksheet Answer Key: problems 6–10
Problem 6: Area and perimeter together
- Area: \(10 \times 4 = 40\) sq ft. Perimeter: \(2 \times 10 + 2 \times 4 = 28\) ft.
- Area: \(11 \times 5 = 55\) sq ft. Perimeter: \(2 \times 11 + 2 \times 5 = 32\) ft.
- Area: \(14 \times 6 = 84\) sq ft. Perimeter: \(2 \times 14 + 2 \times 6 = 40\) ft.
- Area: \(20 \times 8 = 160\) sq ft. Perimeter: \(2 \times 20 + 2 \times 8 = 56\) ft.
40 sq ft and 28 ft; 55 sq ft and 32 ft; 84 sq ft and 40 ft; 160 sq ft and 56 ft
Problem 7: Missing side from area
- \(56 : 8 = 7\). Check: \(7 \times 8 = 56\).
- \(63 : 9 = 7\). Check: \(7 \times 9 = 63\).
- \(120 : 12 = 10\). Check: \(10 \times 12 = 120\).
- \(144 : 16 = 9\). Check: \(9 \times 16 = 144\).
7; 7; 10; 9
Problem 8: Missing side from perimeter
- Half of 30 is 15. \(15 – 9 = 6\) in.
- Half of 44 is 22. \(22 – 14 = 8\) in.
- Half of 52 is 26. \(26 – 10 = 16\) in.
- Half of 60 is 30. \(30 – 20 = 10\) in.
6 in; 8 in; 16 in; 10 in
Problem 9: Rectangles with area 12
Find pairs of numbers that multiply to 12: \(1 \times 12\), \(2 \times 6\), \(3 \times 4\).
- \(2 \times 1 + 2 \times 12 = 26\) units
- \(2 \times 2 + 2 \times 6 = 16\) units
- \(2 \times 3 + 2 \times 4 = 14\) units
1 by 12, 2 by 6, and 3 by 4. The 3 by 4 rectangle has the smallest perimeter, 14 units.
Problem 10: Compare two rectangles
Area of A: \(9 \times 4 = 36\) sq ft. Area of B: \(7 \times 6 = 42\) sq ft.
Perimeter of A: \(2 \times 9 + 2 \times 4 = 26\) ft. Perimeter of B: \(2 \times 7 + 2 \times 6 = 26\) ft.
B has the greater area (42 sq ft against 36 sq ft). The perimeters are equal, 26 ft each.
Grade 4 Area Worksheet Answer Key: problems 11–15
Problem 11: Same perimeter
Area of A: \(6 \times 2 = 12\). Area of B: \(5 \times 3 = 15\). Difference: \(15 – 12 = 3\).
B has the greater area, by 3 square units.
Problem 12: Garden plan
Area: \(12 \times 7 = 84\) sq ft.
Fence: \(2 \times 12 + 2 \times 7 = 24 + 14 = 38\) ft.
84 sq ft of garden and 38 ft of fence.
Problem 13: Poster border
Paper: \(18 \times 24 = 432\) sq in.
Ribbon: \(2 \times 18 + 2 \times 24 = 36 + 48 = 84\) in.
432 sq in of paper and 84 in of ribbon.
Problem 14: Buying a rug
Area: \(9 \times 6 = 54\) sq ft.
Cost: \(54 \times \$4 = \$216\).
The rug costs $216.
Problem 15: Laps around the field
One lap: \(2 \times 100 + 2 \times 60 = 200 + 120 = 320\) yd.
Two laps: \(2 \times 320 = 640\) yd.
Liam jogs 640 yards.
Grade 4 Area Worksheet Answer Key: problems 16–20
Problem 16: Bedroom floor
Length: \(108 : 9 = 12\) ft.
Perimeter: \(2 \times 12 + 2 \times 9 = 24 + 18 = 42\) ft.
The room is 12 ft long, and the perimeter is 42 ft.
Problem 17: Dog pen fence
Fence needed: \(2 \times 15 + 2 \times 10 = 30 + 20 = 50\) ft.
Cost: \(50 \times \$3 = \$150\).
The fence costs $150.
Problem 18: Floor tiles
Tiles needed: \(14 \times 9 = 126\).
12 boxes hold \(12 \times 10 = 120\) tiles, which is not enough. 13 boxes hold 130 tiles.
Diego must buy 13 boxes.
Problem 19: Bulletin board trim
Width: \(54 : 9 = 6\) ft.
Perimeter: \(2 \times 9 + 2 \times 6 = 30\) ft.
Strips: \(30 : 5 = 6\).
6 strips are needed.
Problem 20: Doubling the length
Old area: \(8 \times 5 = 40\) sq ft. New length: 16 ft. New area: \(16 \times 5 = 80\) sq ft.
Old perimeter: \(2 \times 8 + 2 \times 5 = 26\) ft. New perimeter: \(2 \times 16 + 2 \times 5 = 42\) ft.
The area doubles (40 to 80 sq ft), but the perimeter does not double (26 to 42 ft).
Grade 4 Area Worksheet Answer Key: problems 21–22
Problem 21: Length is twice the width
Half of 36 is 18. The tape has 3 equal parts, so one part is \(18 : 3 = 6\) ft.
Area: \(12 \times 6 = 72\) sq ft. Check: \(2 \times 12 + 2 \times 6 = 36\).
Width 6 ft, length 12 ft, area 72 sq ft.
Problem 22: Painting a wall
Wall: \(12 \times 8 = 96\) sq ft. Door: \(3 \times 7 = 21\) sq ft.
Paint: \(96 – 21 = 75\) sq ft.
Noah paints 75 square feet.
How to use this grade 4 area worksheet answer key
Read this grade 4 area worksheet answer key after trying each problem yourself, and redo any problem you missed.
See every chapter on the Grade 4 math page.