Class 8 · English Version · Mathematics
2026 Class 8 Mathematics · English Version · Chapter 3 · Chapter companion part
Explain square units, find direct and reverse areas, use land conventions and distinguish area from perimeter.
Class 8 English Version: part B of the Measurement companion. Eight sections, 30 written tasks and a notebook challenge. Selected companion coverage, not complete textbook coverage. Use all four parts for the mapped chapter methods; these fresh tasks do not reproduce every printed question. Drawings and explanations need guardian or teacher review.
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Perimeter is boundary length; area is the amount of flat surface covered. A 6 m by 4 m rectangle has perimeter 2(6 + 4) = 20 m and area 6 × 4 = 24 m². A square of side s has perimeter 4s and area s². Doubling every length doubles perimeter but multiplies area by four.
A triangle of base b and perpendicular height h has area bh/2. Pair two identical triangles into a parallelogram or rectangle to explain the half. A sloping side is not generally the height. With b = 12 m and h = 5 m, area is 30 m². Reverse the relation as h = 2A/b when b is nonzero.
One metre is 100 cm, so a square metre is 100 × 100 = 10000 cm². Adjacent metric area levels based on a tenfold length change differ by 100. One are is 100 m²; one hectare (ha) is 100 ares = 10000 m². One square kilometre is 100 hectares. Use ha rather than the book’s spelling hector.
One square foot is 12² = 144 square inches; one square yard is 3² = 9 square feet. From the international inch, one square inch is exactly 6.4516 cm²; a square yard is 0.83612736 m². An acre defined as 4840 international square yards is 4046.8564224 m², approximately 4046.86 m². Distinguish this classroom international-yard convention from an old U.S. survey-foot acre.
For this chapter’s local classroom chain, 1 ganda = 324 in² = 2.25 ft²; 20 ganda = 45 ft² per chatak; 16 chatak = 720 ft² per katha; 20 katha = 14400 ft² per bigha. One decimal is 1/100 acre = 435.6 ft². These are the stated source conventions, not a universal rule for regional property records.
For a rectangle with length 3 times breadth x and area 192 m², 3x² = 192, so x = 8 m and length is 24 m. Take the positive root for a physical length. If length exceeds breadth by 4 m and perimeter is 40 m, l + b = 20 and l − b = 4, giving l = 12 and b = 8. Verify both conditions.
Measure a book cover or table in one consistent unit, then multiply the perpendicular lengths. A diagonal across a rectangle uses d² = l² + b², a later-chapter relation supplied here as an extension. For a 12 m by 5 m rectangle, d = 13 m; its perimeter is 34 m and area 60 m². Those quantities answer different questions. Do not use a diagonal as a rectangle’s breadth.
Printed example 6 converts 40 m by 30 m 30 cm to 1212 m²; its intermediate line drops the square symbol and says metres. The area is still a square quantity. For a task using 2.47 acres per hectare, 700/2.47 is about 283.40 ha and rounds to 283 ha. A modern exact-acre calculation can differ slightly: state the factor requested rather than silently changing it. Area conversion does not settle a land title or legal survey.
A triangle has area 90 m² and base 15 m. Since A = bh/2, height h = 2A/b = 180/15 = 12 m. Check: 15 × 12/2 = 90 m²; a sloping edge need not be 12 m.
The grid and height diagrams show mathematical relationships, not a legal plot survey. Read dimensions from labels rather than measuring your phone screen.
Write 1212 m² rather than 1212 m. An area rate in Tk/m² and a fence rate in Tk/m cannot be substituted for each other.
For Exercise 3(4), use 1 acre = 4840 international yd² and 1 yd = 0.9144 m. Ten acres are 40468.564224 m². With length four times breadth, 4b² equals this area: b = 100.584 m and length = 402.336 m, or 402.34 m to two decimal places. The printed 402.31 m does not match this conversion. A calculation using a different rounded source factor must name that factor. Do not round intermediate lengths and then call the final result exact.
Each tenfold change in side length gives a hundredfold change in area.
| Area unit | Equivalent | How to read it |
|---|---|---|
| 1 dm² | 100 cm² | 10 cm × 10 cm |
| 1 m² | 100 dm² = 10000 cm² | 100 cm × 100 cm |
| 1 are | 100 m² | 10 m × 10 m |
| 1 hectare | 100 ares = 10000 m² | 100 m × 100 m |
| 1 km² | 100 hectares = 1000000 m² | 1000 m × 1000 m |
For 0.4 km² use 0.4 × 100 = 40 hectares. For 2.5 m² use 2.5 × 10000 = 25000 cm².
Local rows use the source chapter’s classroom chain, not a universal survey rule.
| Unit | Square feet or inches | Equivalent relationship |
|---|---|---|
| 1 ganda / square arm | 324 in² = 2.25 ft² | 1.5 ft × 1.5 ft |
| 1 chatak | 45 ft² | 20 ganda |
| 1 katha | 720 ft² | 16 chatak |
| 1 bigha | 14400 ft² | 20 katha |
| 1 acre | 43560 ft² | 4840 international yd² = 100 decimals |
| 1 decimal | 435.6 ft² | 1/100 acre = 1000 square kari in the source chain |
| 1 kari | 0.66 ft | 100 kari = 66 ft; square this length for square kari |
| 1 square statute mile | 27878400 ft² | 640 acres = 1936 source-convention bigha |
Three katha give 3 × 720 = 2160 ft². One square metre is about 10.7639 ft², 4.78396 ganda or 0.239198 chatak in this chain. One are is about 23.9198 chatak. One acre is 3 bigha 8 chatak under this same chain. Keep rounded comparisons labelled.
Use perpendicular lengths in compatible units.
Rectangle: A = lb; P = 2(l + b) Square: A = s²; P = 4s Triangle: A = bh/2; h = 2A/b If l = kb: b = √(A/k), l = kb
A sloping triangle side is not generally its height. Use a positive root for a physical length.
Square the entire length factor rather than moving the decimal once.
1 in² = (2.54 cm)² = 6.4516 cm² 1 yd² = (0.9144 m)² = 0.83612736 m² 1 acre = 4840 × 0.83612736 m² = 4046.8564224 m²
An old survey-foot-based acre differs slightly. Use the task’s stated convention; never silently mix different acre factors.
This is the later-chapter right-triangle relationship, introduced only to interpret the sample question.
d² = l² + b² d = √(l² + b²)
The diagonal does not replace the breadth in an area formula. A full proof belongs to the later Pythagoras chapter.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original exact rectangular grid: every cell is the same square unit. Display pixels are a model, not a physical metre scale.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original geometric model with one consistent drawing scale for the triangle and its perpendicular height. The bounding rectangle explains the half; it is not a second measured plot.
Show your working on paper. Check your answer, then choose Next.
24
6 × 4 = 24 m².
20
2(6 + 4) = 20 m.
49
7² = 49 m².
30
12 × 5/2 = 30 m².
12
2 × 84/14 = 12 m.
25000
2.5 × 10000 = 25000 cm².
300
3 × 100 = 300 ares.
40
0.4 × 100 = 40 ha.
12.9032
2 × 2.54² = 12.9032 cm².
2178
5 × 435.6 = 2178 ft².
2160
3 × 720 = 2160 ft².
50
2.5 × 20 = 50 katha.
8
3b² = 192, so b² = 64 and positive b = 8 m.
13
d² = 144 + 25 = 169, so d = 13 m.
102
8 m 50 cm = 8.5 m; 12 × 8.5 = 102 m².
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Draw 24 squares in 6 columns and 4 rows. Count the boundary as 6 + 4 + 6 + 4 = 20 units. Interior count is 24 square units.
Check that boundary edges are not counted as unit squares.
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Pair the triangles to make a parallelogram of base b and perpendicular height h. The whole has area bh, so one has bh/2. Mark a right angle at the height.
A sloping side used as height without justification is incorrect.
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Height = 7.5 m. Area = 16 × 7.5/2 = 60 m².
Convert mixed units before multiplication and label the perpendicular height.
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The unit square is 100 cm along each of two perpendicular sides, so it contains 100 × 100 = 10000 unit cm² squares.
Use both dimensions or a labelled grid rather than only quoting the result.
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One yard = 0.9144 m, so square yard = 0.9144² = 0.83612736 m². Multiply by 4840 to get 4046.8564224 m², or 4046.86 m² rounded to two decimals.
Name the international-yard convention and round only at the end.
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One ganda = 324 in²/144 = 2.25 ft². Twenty ganda make 45 ft² per chatak; sixteen chatak make 720 ft² per katha; twenty katha make 14400 ft² per bigha.
Do not use the source’s square-inch count as a square-foot count.
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43560/100 = 435.6 ft² per decimal. Five decimals give 2178 ft².
Explain that decimal is a land-area unit here, not the decimal-point operation.
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Let breadth b > 0. Then length = 3b and 3b² = 192. Thus b = 8 m and length = 24 m. Check 24 × 8 = 192.
Use the positive root and verify the ratio as well as area.
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l + b = 20 and l − b = 4. Hence l = 12 m and b = 8 m. Area is 96 m², a separate quantity.
Require the perimeter relation and a check.
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Both areas are 24 m². Perimeters are 20 m and 22 m. Equal area does not force equal boundary length.
Explain what each result measures.
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Measure length and breadth with stated resolution, multiply for cm², then divide by 10000 for m². Actual dimensions must come from your measurement.
Check tool alignment, compatible units and realistic precision.
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The 13 m is the diagonal from sqrt(12² + 5²); 34 m is the perimeter; 60 m² is covered area.
Use a labelled sketch to identify each quantity.
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494/2.47 = 200 ha under that supplied approximation. The result uses the given factor, not an assertion that 2.47 is exact.
State the convention and avoid replacing it without explanation.
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30 m 30 cm = 30.3 m. Product = 1212 m², also 12 ares 12 m². The numeric product is correct but the linear unit is wrong.
Identify the missing squared unit and show the conversion.
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Names such as katha and bigha can be used with regional conventions. This lesson states 720 ft² per katha and 20 katha per bigha for its classroom problems. A real property record must be interpreted from its own applicable survey information.
Do not claim one classroom chain determines every property area.
Draw one rectangle and one triangle, and create a land-unit conversion card using explicit conventions.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
This original Kidemy practice follows the topic order of 2026 Class 8 Mathematics · English Version, chapter 3, printed pages 29–47. It does not replace the complete chapter or its practical teaching.
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