Question Quilt lace
Which lace roll covers the whole quilt border?
Steps only
The border totals 50 units.
Answer
The 50-unit green lace.
CLASS 5 · MATHS MELA · CHAPTER 11
Grandmother’s Quilt
Measure perimeter and area with tiles and grids, compare shapes and apply rectangle and square formulas to practical objects.
46 worked answersAll 4 exercise sets
What you will learn
- Distinguish boundary length from covered area.
- Measure irregular and regular regions using square units.
- Use rectangle and square formulas and explain area–perimeter relationships.
46 worked answers · short steps first, explanations when you need them
Quilt Border and Tiling Area
Textbook pages 142–143
Question Two laces
If two colours share the 50-unit border equally, how much of each is needed?
Steps only
50÷2=25.
Answer
25 units of each colour.
Question 1(a)
Find the perimeter of an equal-sided pentagon with side 4 cm.
Steps only
5×4=20.
Answer
20 cm.
Question 1(b)
Find the perimeter of two equal-sided triangles touching at one vertex, each side 5 cm.
Steps only
All six triangle sides lie on the outside.
6×5=30.
Answer
30 cm.
Question 2(a)
Give two rectangles with perimeter 26 cm.
Steps only
2(L+B)=26, so L+B=13.
Answer
Examples: 6 cm×7 cm and 5 cm×8 cm.
Question 2(b)
Give two rectangles with perimeter 18 cm.
Steps only
2(L+B)=18, so L+B=9.
Answer
Examples: 4 cm×5 cm and 3 cm×6 cm.
Question Rug patches
How many square patches are in the pictured rug?
Steps only
Count 4 rows and 14 patches per row.
4×14=56.
Answer
56 patches.
Question Tiling shapes
Which table-cover shapes leave no gaps?
Steps only
Triangles, squares and rectangles meet edge-to-edge.
Circles leave curved gaps.
Answer
Triangles, squares and rectangles tile; circles do not.
Question Table 1
How many triangular tiles cover Table 1?
Steps only
The table has 10 square regions, each split into 2 triangles.
10×2=20.
Answer
20 triangle units.
Question Table 3
How many square tiles cover Table 3?
Steps only
Count 2 rows of 5.
Answer
10 square units.
Question Table 4
How many rectangular tiles cover Table 4?
Steps only
Count 4 rows of 5 small rectangles.
Answer
20 rectangle units.
Question Circles
Can equal circles cover a flat table without gaps?
Steps only
Touching circles leave curved spaces between them.
Answer
No, circles alone do not tile the plane.
Question Real objects
Which same-sized objects can cover a table completely?
Steps only
Arrange notebooks, lunch boxes, pencil boxes or textbooks edge-to-edge.
Record whether gaps or overlaps remain.
Answer
Rectangular objects can cover it if their dimensions fit the table in whole rows and columns; the observed answer depends on the objects and table.
Comparing Areas on Grids
Textbook pages 144–146
Question Desk area
Find the area of the pictured desk grid.
Steps only
There are 9 columns and 6 rows.
9×6=54.
Answer
54 square units.
Question Green triangles
How many small green triangles cover the desk?
Steps only
One green triangle is half a grid square.
54×2=108.
Answer
108 green triangles.
Question Red triangles
How many large red triangles cover the desk?
Steps only
The red right triangle has base and height 3 units, so its area is 3×3÷2=4.5 square units.
54÷4.5=12.
Answer
12 red triangles.
Question Blue squares
How many blue squares cover the desk?
Steps only
One blue tile equals one grid square.
Answer
54 blue squares.
Question Rectangles A–C
Compare the three rectangles on the grid.
Steps only
A=3×4=12; B=2×4=8; C=2×5=10.
Answer
A has the largest area; A>C>B.
Question Garden A
Find Garden A’s area.
Steps only
It covers 2 columns×5 rows.
Answer
10 cm².
Question Garden B
Find Garden B’s area.
Steps only
It covers 4 columns×3 rows.
Answer
12 cm².
Question Garden comparison
Which garden is larger and by how much?
Steps only
12−10=2.
Answer
Garden B by 2 cm².
Question Palm
Estimate a traced palm’s area on a 1 cm grid.
Steps only
Count fully covered squares.
Combine partly covered squares into approximate whole squares.
Answer
Student-specific; approximate area=full squares+about half of the boundary squares.
Question Leaves
Compare leaf areas on a grid.
Steps only
Use the same full-square and partial-square method for every leaf.
Answer
The leaf with the greatest estimated square count is largest; the least count is smallest.
Area and Perimeter Relationships
Textbook pages 147–150
Question Mat (a)
Find area and perimeter of the 5-by-2 patch mat.
Steps only
Area=5×2=10.
Perimeter=2(5+2)=14.
Answer
Area 10 square units; perimeter 14 units.
Question Mat (b)
Find area and perimeter of the 4-by-3 patch mat.
Steps only
Area=4×3=12.
Perimeter=2(4+3)=14.
Answer
Area 12 square units; perimeter 14 units.
Question Trisha claim
Does increasing area always increase perimeter?
Steps only
The two mats have areas 10 and 12 but both perimeters are 14.
Answer
No.
Question Explore 1 · same area
Which labelled green shapes have the same area?
Steps only
Count shaded unit squares.
Shapes (a), (c), (d) and (f) each contain 12 squares.
Answer
(a), (c), (d) and (f), each area 12 cm².
Question Explore 1 · perimeters
Compare perimeters of the 12-square shapes.
Steps only
(a), a 6×2 rectangle, has perimeter 16.
(c) and (d), 3×4 and 4×3 rectangles, have perimeter 14.
(f), a 1×12 strip, has perimeter 26.
Answer
Perimeters are 16, 14, 14 and 26 cm respectively.
Question Explore 2 · first group
Which red shapes share perimeter 12?
Steps only
For each shape use P=4n−2e, where n is squares and e is shared edges.
Answer
Shapes (a) and (b), each with perimeter 12 cm.
Question Explore 2 · second group
Which red shapes share perimeter 16?
Steps only
Count outside edges for the cross, L and strip.
Answer
Shapes (c), (d) and (e), each with perimeter 16 cm.
Question Explore 2 · areas
Find the areas of red shapes (a)–(e).
Steps only
Count shaded unit squares in each.
Answer
Each shape has area 7 cm².
Question Same area drawing
Draw shapes with the same area as the 2×9 rectangle.
Steps only
Given area=2×9=18 cm², perimeter=22 cm.
A 3×6 rectangle also has area 18 and perimeter 18.
A 1×18 rectangle has area 18 and perimeter 38.
Answer
Examples: 3×6 and 1×18; all have area 18 cm² but different perimeters.
Question Square and triangle
Is the 3×3 square’s area less than the triangle shown?
Steps only
Square area=3×3=9.
Triangle base=6 and height=3, so area=6×3÷2=9.
Answer
No; their areas are equal at 9 cm².
Question Patchwork
How many patches make a 6-by-4 rectangle?
Steps only
6×4=24.
Answer
24 patches.
Rectangle Formulas and Measurement
Textbook pages 151–154
Question Square example
Find area and perimeter of a 5 cm square.
Steps only
Area=5×5=25.
Perimeter=4×5=20.
Answer
25 cm² and 20 cm.
Question Classroom
Find a classroom floor’s area and perimeter.
Steps only
Measure length L and breadth B in metres.
Area=L×B; perimeter=2(L+B).
Answer
Student-specific; report L×B m² and 2(L+B) m.
Question 2(a)
Find area and perimeter of the 6 cm by 6 cm grid rectangle.
Steps only
Area=6×6=36.
Perimeter=2(6+6)=24.
Answer
36 cm²; 24 cm.
Question 2(b)
Find area and perimeter of the 4 cm by 7 cm grid rectangle.
Steps only
Area=4×7=28.
Perimeter=2(4+7)=22.
Answer
28 cm²; 22 cm.
Question 2(c)
Find area and perimeter of the 12 cm by 4 cm grid rectangle.
Steps only
Area=12×4=48.
Perimeter=2(12+4)=32.
Answer
48 cm²; 32 cm.
Question 2(d)
Find area and perimeter of the 3 cm by 3 cm grid rectangle.
Steps only
Area=3×3=9.
Perimeter=2(3+3)=12.
Answer
9 cm²; 12 cm.
Question 2(e)
Find area and perimeter of the 6 cm by 5 cm grid rectangle.
Steps only
Area=6×5=30.
Perimeter=2(6+5)=22.
Answer
30 cm²; 22 cm.
Question Objects table
Measure notebook, newspaper, blackboard, Ludo board and two other rectangles.
Steps only
For each object record length L and breadth B in the same unit.
Calculate L×B and 2(L+B).
Answer
Answers depend on the measured objects; include dimensions, square units for area and length units for perimeter.
Question 4
Find area of a 42 m by 34 m field.
Steps only
42×34=42×30+42×4=1,260+168.
Answer
1,428 m².
Question 5
A garden area is 64 m² and length 16 m. Find breadth.
Steps only
64÷16=4.
Answer
4 m.
Question 6
Find area of the marked 32 cm wide figure with heights 6 cm and 12 cm.
Steps only
Total height=6+12=18 cm.
Area=32×18.
Answer
576 cm².
Question Tile game
How is the perimeter updated when adding a unit tile?
Steps only
An isolated tile adds 4 edges.
For every edge it shares with the existing figure, subtract 2 from that increase.
Answer
New perimeter=old perimeter+4−2×shared edges; the first player to make 24 wins.