Area and Perimeter Practice Worksheets
Separate inside squares from outside distance, then work through rectangles, triangles, composite shapes, and same-perimeter comparisons.
Try each area or perimeter problem, then open the answer.
1. A rectangle is 8 units long and 3 units wide. Find the area.
24 square units. Area of a rectangle is length × width, so 8 × 3 = 24.
2. A rectangle is 8 units long and 3 units wide. Find the perimeter.
22 units. Perimeter is the distance around: 2 × (8 + 3) = 2 × 11 = 22.
3. A square has side length 6. Find its area and perimeter.
Area = 36 square units and perimeter = 24 units. Area is 6 × 6 = 36; perimeter is 4 × 6 = 24.
4. A rectangle has area 45 square units and width 5. What is its length?
9 units. Since area = length × width, 45 = length × 5, so length = 45 ÷ 5 = 9.
5. A rectangle has perimeter 30 units and length 9 units. What is its width?
6 units. Perimeter = 2(l + w), so 30 = 2(9 + w). Divide by 2: 15 = 9 + w, so w = 6.
6. A triangle has base 10 and height 6. Find its area.
30 square units. Triangle area is (base × height) ÷ 2, so (10 × 6) ÷ 2 = 30.
7. A right triangle has legs 7 and 4. Find its area.
14 square units. Use one leg as the base and the other as the height: (7 × 4) ÷ 2 = 14.
8. A rectangle is 12 by 5. A 3 by 2 corner is removed. Find the remaining area.
54 square units. The full rectangle is 12 × 5 = 60. The removed corner is 3 × 2 = 6. Remaining area is 60 − 6 = 54.
9. An L-shape is made from a 6 by 4 rectangle and a 3 by 2 rectangle that do not overlap. Find the total area.
30 square units. Add the two areas: 6 × 4 = 24 and 3 × 2 = 6, so 24 + 6 = 30.
10. A garden is 10 units by 4 units. A fence goes around it. How much fence is needed?
28 units. Fence length is perimeter: 2 × (10 + 4) = 28.
11. Which rectangle has larger area: 9 by 4 or 8 by 5?
The 8 by 5 rectangle. Its area is 40 square units, while 9 × 4 = 36 square units.
12. Which rectangle has larger perimeter: 9 by 4 or 8 by 5?
They have the same perimeter. 2 × (9 + 4) = 26 and 2 × (8 + 5) = 26.
13. A shape covers 18 unit squares on a grid. What is its area?
18 square units. Area counts the number of unit squares inside the shape.
14. A 5 by 5 square has a 2 by 2 square removed from the middle. Find the remaining area.
21 square units. The large square area is 25. The removed square area is 4. Remaining area is 25 − 4 = 21.
15. Two rectangles both have perimeter 20. Rectangle A is 6 by 4. Rectangle B is 8 by 2. Which has more area?
Rectangle A. Both perimeters are 20, but A has area 24 and B has area 16. Same perimeter does not always mean same area.
Area and perimeter questions
What is the difference between area and perimeter?
Perimeter is the distance around a shape. Area is the number of square units inside the shape.
What formulas should my child know first?
For rectangles, use A = length × width and P = 2(length + width). For triangles, use A = base × height ÷ 2.
Why do area and perimeter get confused?
They can use the same side lengths, but they ask different questions. Area counts squares inside; perimeter counts the outside boundary.
How should we practice without turning it into busywork?
Keep it untimed. Ask your child to say whether the problem wants inside squares or outside distance before calculating. That habit prevents most mix-ups.
Preparing for a gifted & talented test? Many tests like the CogAT® include reasoning problems like these — see free CogAT-style sample questions →