Chapter 11 of Class 5 Maths, Grandmother’s Quilt, uses a patchwork quilt made of stitched-together fabric squares and shapes to introduce area and perimeter – measuring the boundary and surface covered by a shape using grid squares and simple formulas.
Key Concepts
What Perimeter Means
Perimeter is the total distance around the outer boundary of a shape – found by adding up the lengths of all its sides. For a rectangle, perimeter = 2 × (length + breadth); for a square, perimeter = 4 × side.
What Area Means
Area is the amount of flat surface a shape covers, usually measured in square units (like square centimetres). On a grid, area can be found by counting the number of unit squares a shape covers.
Area of a Rectangle and Square
For a rectangle, area = length × breadth. For a square (where all sides are equal), area = side × side. These formulas come from counting how many unit squares fit into rows and columns inside the shape.
Area of Irregular Shapes on a Grid
For shapes that are not perfect rectangles (like quilt patches with uneven edges), area is estimated by counting full squares as 1 unit each and combining part-squares that look like they could pair up to make roughly a full square, giving an approximate total area.
Perimeter vs. Area – Different Measures
Perimeter and area measure two different things and are not directly related in a simple way – two shapes can have the same perimeter but different areas, or the same area but different perimeters, depending on their shape.
Combining Patches (Composite Shapes)
A quilt made of several joined squares and rectangles can have its total area found by adding the areas of each individual patch, and its perimeter found by tracing only the outer boundary of the whole combined shape (not the internal stitching lines between patches).
Worked Examples
Example 1: Perimeter of a Rectangle
A quilt patch is 8 cm long and 5 cm wide. Find its perimeter.
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm.
Example 2: Area of a Square
A square patch has each side 6 cm. Find its area.
Area = 6 × 6 = 36 sq cm.
Example 3: Same Perimeter, Different Area
Compare a 6 cm × 4 cm rectangle and an 8 cm × 2 cm rectangle. Do they have the same perimeter? Do they have the same area?
Perimeters: 2×(6+4)=20 cm and 2×(8+2)=20 cm – the same. Areas: 6×4=24 sq cm and 8×2=16 sq cm – different, showing equal perimeter does not mean equal area.
Quick Recap
- Perimeter = total distance around a shape’s boundary (add up all sides).
- Area = the flat surface a shape covers, measured in square units.
- Rectangle area = length × breadth; rectangle perimeter = 2 × (length + breadth).
- Square area = side × side; square perimeter = 4 × side.
- Same perimeter does not guarantee the same area, and same area does not guarantee the same perimeter.
- For a shape made of joined patches, add up individual areas but trace only the outer edge for perimeter.
Common Mistakes to Avoid
- Confusing perimeter (a length, measured in cm/m) with area (a surface, measured in square cm/m) – they use different units.
- Forgetting to multiply by 2 when finding a rectangle’s perimeter (adding length + breadth only once).
- Counting internal stitching or dividing lines as part of the perimeter of a combined quilt shape.
- Miscounting part-squares on a grid when estimating the area of an irregular shape.
- Assuming a bigger perimeter always means a bigger area, which is not always true.
Home Practice Tips
- Measure the length and breadth of a real book, notebook, or tabletop, then calculate both its area and perimeter.
- Draw a few different rectangles on graph paper that all have the same perimeter, then compare their areas.
- Trace an irregular leaf or hand outline on graph paper and estimate its area by counting full and part squares.
- If there’s a patchwork or tiled item at home, identify individual patches/tiles and add up their areas to estimate the whole.
- Use string to measure the perimeter of a curved object (like a plate) by wrapping it around the edge and then measuring the string.
Frequently Asked Questions
Q1. Why is area measured in square units but perimeter in regular units?
Perimeter is a length (one dimension – distance around the edge), while area covers a two-dimensional surface, so it needs a unit that accounts for both length and width, which is why square units (like sq cm) are used.
Q2. How can two shapes have the same perimeter but different areas?
Because perimeter only measures the boundary length, while area depends on how that boundary encloses space – a long, thin rectangle and a more square-shaped rectangle can share a perimeter but enclose very different amounts of surface.
Q3. How do you find the area of a shape that isn’t a perfect rectangle or square?
Place it on a grid and count the number of full unit squares it covers, combining part-squares in pairs that together look roughly like a full square, to estimate the total area.
Q4. Why does perimeter only count the outer boundary of a combined shape?
Because perimeter measures the distance you would walk if tracing only the outside edge of the whole shape; internal lines between joined patches are inside the figure, not part of its outer boundary.
Q5. What real-life situations use area and perimeter like this chapter?
Perimeter is used for things like fencing a garden or framing a picture, while area is used for things like buying carpet, tiles, or fabric – exactly the kind of quilt-making context this chapter is built around.
Full walkthrough: Chapter 11 Solutions · Extra Questions.
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