**Perimeter and Area Basics**
**Definitions:**
Perimeter = total distance around shape border (measured in cm or m)
Area = space inside shape (measured in square cm or square m)
**Key Formulas:**
Rectangle Perimeter = 2L + 2B or add all 4 sides
Rectangle Area = L × B (Length × Breadth)
Square Perimeter = 4 × side
Square Area = side × side
**What Tiles (Covers with No Gaps):**
Squares ✓ Rectangles ✓ Triangles ✓
Circles ✗ (leaves gaps)
**Important Idea:**
Same area ≠ same perimeter
Same perimeter ≠ same area
**Real Examples:**
Quilt border needs lace = PERIMETER problem
Quilt patches covering = AREA problem
Classroom floor coverage = AREA problem
Garden fencing = PERIMETER problem
**Unit Square:** A square with 1 cm sides = 1 square cm area
**Don't Confuse:** Perimeter counts edges (1D), area fills space (2D).
Q1. What is the perimeter of a square with side 5 cm?
Answer: A — Perimeter of square = 4 × side = 4 × 5 = 20 cm.
Q2. Which shape leaves gaps when tiling a table?
Answer: B — Circles have curved edges that leave gaps between them, so they cannot tile perfectly.
Q3. A rectangular garden has length 8 m and breadth 6 m. What is its area?
Answer: C — Area of rectangle = Length × Breadth = 8 × 6 = 48 square m.
Q4. Grandmother wants to put lace around the border of her quilt. Does she need to find the _____ or area?
Answer: A — Border means the edge around the quilt, which is the perimeter.
Q5. What is the area of a square with side 7 cm?
Answer: B — Area of square = side × side = 7 × 7 = 49 square cm.
Q6. Two shapes have the same area. Will they always have the same perimeter?
Answer: B — Same area does not mean same perimeter; different shapes can have same area but different perimeters.
Q7. A rectangle has length 10 cm and breadth 4 cm. What is its perimeter?
Answer: B — Perimeter = 2 × Length + 2 × Breadth = 2(10) + 2(4) = 20 + 8 = 28 cm.
Q8. To cover the floor of a classroom with square tiles, which do you need to find?
Answer: B — Covering the floor means filling the space inside, which requires area calculation.
Q9. In the figure below, the rectangle has length 12 cm and breadth 5 cm. What is its area?
Answer: B — Area = Length × Breadth = 12 × 5 = 60 square cm.
Q10. Which measurement tells you how much lace is needed to decorate the border of a quilt cover?
Answer: B — The border is the outer edge, and the distance around it is the perimeter.
What is perimeter?
Perimeter is the total distance around the border of any shape.
What is area?
Area is the amount of space covered inside a shape.
Formula for perimeter of rectangle
Perimeter of rectangle = 2 × Length + 2 × Breadth or add all 4 sides.
Formula for area of rectangle
Area of rectangle = Length × Breadth.
Formula for perimeter of square
Perimeter of square = 4 × Length of one side.
Formula for area of square
Area of square = Length × Length.
What is 1 unit square?
1 unit square is a square with sides 1 unit long, used as a standard to measure area.
Which shapes tile without gaps?
Squares, rectangles, and triangles can tile together without gaps or overlaps.
Why use square grid to find area?
Square grids are the most convenient because squares have equal sides and fit together perfectly.
Can same area have different perimeter?
Yes, two shapes can have the same area but different perimeters.
What is perimeter? [1 mark]
It is the total distance around the outside border of any shape. Give the definition only.
A square has a side of 6 cm. Find its perimeter and area. [2 marks]
Use Perimeter of square = 4 × side and Area of square = side × side. Show both calculations.
Grandmother wants to put lace around her quilt border and also use patches to fill the quilt surface. Explain why she needs to find both perimeter and area, and give one example for each from your home. [3 marks]
Perimeter = distance around edge (for lace on border). Area = space inside (for patches covering). Use real examples like table, notebook, or floor.
A rectangular classroom has length 12 m and breadth 8 m. The teacher wants to put tiles on the floor and a border strip around the walls. Calculate (a) the area of the floor, (b) the perimeter of the floor, and (c) explain which measurement is needed for tiles and which for the border strip. [5 marks]
For area, use L × B. For perimeter, use 2L + 2B. Then explain: area for floor tiles (filling space), perimeter for border strip (around edge).
True or False: Two shapes can have the same area but different perimeters. Justify your answer with an example. [2 marks]
Think of different rectangles with same area but different length and breadth. Show one example with numbers and calculation.
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