Mathematics Worksheet: Area & Perimeter (Preparatory Stage)
Based on NCERT/CBSE and “Grandmother’s Quilt” chapter. Attempt all 30 questions—answers are shown with a button and each detailed solution is hidden for discovery!
Concepts (Area & Perimeter)
- What do we call the length of the border of a shape?
Show Answer
Answer: PerimeterShow Solution
Solution: Perimeter is the total length of all sides of a shape. - The area of a square is measured in which units?
Show Answer
Answer: Square units (cm², m²)Show Solution
Solution: Area = length × breadth; measured in “square” units. - If all four sides of a rectangle are equal, what shape is it?
Show Answer
Answer: SquareShow Solution
Solution: A rectangle with all sides equal is a square. - What do you call the region covered by a figure?
Show Answer
Answer: AreaShow Solution
Solution: Area is the measure of space inside a shape. - Name two shapes that can tile a table without gaps.
Show Answer
Answer: Squares, rectanglesShow Solution
Solution: From NCERT: squares and rectangles cover a table completely (triangles work too). - How is the area of a rectangle found?
Show Answer
Answer: Length × BreadthShow Solution
Solution: Area = length × breadth (from patchwork/rug activities). - Define “unit square” for measuring area.
Show Answer
Answer: A square with sides 1 unit longShow Solution
Solution: Covers exactly 1 unit of space; used as a reference for measuring. - Which shape gives largest area for same perimeter: square or rectangle?
Show Answer
Answer: SquareShow Solution
Solution: For a fixed perimeter, square encloses the most area (visualize cutting and re-pasting). - If you cover a table with circles, will there be gaps?
Show Answer
Answer: YesShow Solution
Solution: Circles do not tile — there will be spaces between them (as in the book table example). - If a rectangle is 6 by 4 squares, what is its area?
Show Answer
Answer: 24 square unitsShow Solution
Solution: 6 × 4 = 24 (counting patches as shown in “length × breadth”).
Computational Skills
- Find the perimeter of a square with sides 5 cm.
Show Answer
Answer: 20 cmShow Solution
Solution: 4 sides × 5 = 20 cm (all sides equal). - What is the area of a rectangle 8 cm long and 3 cm wide?
Show Answer
Answer: 24 cm²Show Solution
Solution: 8 × 3 = 24 cm² (length × breadth). - Draw two rectangles with perimeter 18 cm on grid paper. (Write possible sides.)
Show Answer
Answer: (a) 5 cm × 4 cm (b) 7 cm × 2 cmShow Solution
Solution: 2 × (5+4) = 18; 2 × (7+2) = 18 - If a square covers 1 unit, how many squares cover a table with area 20?
Show Answer
Answer: 20 squaresShow Solution
Solution: Area = number of tiles × area per tile = 20 × 1 = 20 units. - Find the area and perimeter of a rug made with 6 rows × 5 square patches.
Show Answer
Answer: Area = 30, Perimeter = 22 patchesShow Solution
Solution: 6 × 5 = 30 for area; Perimeter = 2×(6+5) = 22 patches. - If the area of a square is 36 cm², what is the length of each side?
Show Answer
Answer: 6 cmShow Solution
Solution: √36 = 6; Area = side × side. - How many square tiles of 1 cm² are needed for an area of 48 cm²?
Show Answer
Answer: 48 tilesShow Solution
Solution: 48 / 1 = 48 tiles. - The length of a rectangular field is 20 m and breadth is 13 m. Find area.
Show Answer
Answer: 260 m²Show Solution
Solution: 20 × 13 = 260. - Perimeter of a rectangle = 2 × (length + ...?)
Show Answer
Answer: BreadthShow Solution
Solution: Perimeter = 2 × (length + breadth). - If you double the sides of a square, by what factor does its area increase?
Show Answer
Answer: 4 timesShow Solution
Solution: Area = side²; (2×side)² = 4 × (side²).
Problem Solving & Real-World Modeling
- If a quilt border is 40 units, which laces can cover it? (Red: 40, Green: 50, Blue: 25 units)
Show Answer
Answer: Red lace or part of green laceShow Solution
Solution: Red = exact; Green = longer, can cut extra. - Find the area and perimeter of a square with 7 cm sides.
Show Answer
Answer: Area = 49 cm²; Perimeter = 28 cmShow Solution
Solution: Area: 7 × 7; Perimeter: 4 × 7. - Draw two rectangles on a square grid each with area 24 cm². (Write possible lengths and breadths.)
Show Answer
Answer: (a) 6 × 4; (b) 8 × 3; (c) 12 × 2Show Solution
Solution: Area = length × breadth. - A garden is 9 m × 6 m; how many 1 m² tiles are needed for the area?
Show Answer
Answer: 54 tilesShow Solution
Solution: 9 × 6 = 54; Each tile = 1 m². - If a notebook cover measures 21 cm × 15 cm, find area and perimeter.
Show Answer
Answer: Area = 315 cm²; Perimeter = 72 cmShow Solution
Solution: Area: 21 × 15; Perimeter: 2 × (21 + 15). - The area of a rectangular garden is 120 m² and its length is 12 m. What is its breadth?
Show Answer
Answer: 10 mShow Solution
Solution: Area ÷ Length = 120/12 = 10. - Find the perimeter of a classroom 8 m long and 5 m wide.
Show Answer
Answer: 26 mShow Solution
Solution: Perimeter = 2 × (8 + 5) = 26. - Which mat needs more patches: 7 by 5 or 6 by 6? (Find areas)
Show Answer
Answer: 6 by 6 needs more (36 > 35)Show Solution
Solution: 7 × 5 = 35; 6 × 6 = 36. - If one side of a square is 9 cm, what will be the area of the square rug?
Show Answer
Answer: 81 cm²Show Solution
Solution: 9 × 9 = 81. - Challenge: A quilt with a perimeter 32 units uses two types of lace (red: 20, blue: 12). How many of each are needed?
Show Answer
Answer: Red: 20 units; Blue: 12 units.Show Solution
Solution: 20 + 12 = 32; both together cover perimeter.