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CBSE Class 8 · Mathematics

Area

Official NCERT chapter from Ganita Prakash Part II (book code hegp2). ExamMaster notes are original teaching at CBSE Class 8 depth.

This lesson follows the official chapter “Area” in Ganita Prakash Part II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 8
  • Easy level
  • 8 concepts

1Rectangle and Squares

A rectangle’s area is length × breadth in square units. A square is the special case side × side. Count the unit squares if the grid is there; the product is that count.

Adding length and breadth is the perimeter steal.

Figure. Same unit tile on both shapes. The 3-by-2 rectangle holds 6 tiles; the 2-by-2 square holds 4. The square is a rectangle whose sides match. Tile size is to scale across the two shapes.

How it works

  1. Write l and bThe sides.
  2. Multiplyl × b square units.
  3. For a square, side × sideThe special case.

A 7-by-4 rectangle

A rectangle is 7 cm by 4 cm. Find its area and its perimeter.

  • Area7×4=28 cm²
  • Perimeter2(7+4)=22 cm
  • Different unitscover vs walk

Pro tip. Area tiles the inside; perimeter walks the rim.

2Mark what is given on the figure

Mark what is given on the figure: ticks, lengths, a right-box, a height to a base. A length you were not given is not yours to invent. The figure is a record, not a decoration.

A drawing that “looks 5 cm” is not a given 5.

Figure. Before any formula, write the lengths you were given on the figure. This rectangle is 9 by 4 to scale. Walk around is 2(9+4)=26; tiles inside are 9×4=36. Do not swap those two asks.

How it works

  1. Copy every marked length onto your sketchThe given.
  2. Leave unmarked sides unnamedNot yours.
  3. Then choose a formula those marks supportGiven first.

3A definition is a test, not a picture

Area is a test: a count of unit squares (or a taught product that equals that count). A picture of a field is not the area until you have units and a count.

A green shading is not 28 cm².

Figure. The chunky 5-by-3 looks bigger on the page but holds 15 unit tiles. The long 8-by-2 holds 16. Drawn areas are in the 16:15 ratio of those counts. Area is a count, not a glance.

How it works

  1. Name the unit square1 cm², or 1 square on the grid.
  2. Count or compute the productThe test.
  3. Write the unitMute without it.

4Equal marks must be earned

Equal marks must be earned: two ticks mean those sides were given equal. You may not add ticks because the figure looks even. Unearned marks are lies.

A freehand “almost square” is not four ticks.

Figure. Equal-side marks are earned by measuring, not by a glance. The left shape is a true square (sides match after the aspect stretch) and carries a tick on each side. The right block is wider than it is tall and has no ticks yet.

How it works

  1. Use only marks that are drawn or statedEarned.
  2. If you need an equal side, it must be given or provedNot a look.
  3. Refuse extra ticksHonest figure.

5Perimeter is the walk around

Perimeter is the walk around: add the outer sides. A 7-by-4 rectangle walks 7+4+7+4 = 22. Do not multiply for a perimeter.

7 × 4 as a “walk” is the area steal.

Figure. Perimeter is the walk around: 6+4+6+4=20. Area would be 6×4=24 tiles. Same rectangle, two different asks. The 6-by-4 shape is drawn 3:2. Do not feed the walk into the area formula.

How it works

  1. List the outer sidesThe walk.
  2. Add themThe perimeter.
  3. Keep the length-unit, not the square-unitA walk, not a cover.

6Area is the tiles inside

Area is the tiles inside. Gaps and overlaps are not allowed in the count. A triangle on a grid is half a rectangle when that is the taught move — name the half.

Counting only the full squares and ignoring half-squares is an undercount if the lesson used them.

Figure. Area is the tiles that fill the inside. A 4-by-3 grid of equal unit squares holds 12 tiles. One unit is filled so the tile is visible. The walk around would be 14 — a different number, a different ask.

How it works

  1. See the insideThe tiles.
  2. Count full units and taught halvesThe cover.
  3. Write square unitsArea.

7A formula names a count of units

A formula is a named count: A = l × b is “how many unit squares”. If you cannot say what is being counted, the formula is a chant.

Memorising A = l × b with no unit square is a sticker.

Figure. The formula A = l × b is a count of unit tiles: 5 along the length and 3 along the breadth makes 15. The 5-by-3 rectangle is drawn to that ratio. The formula does not invent a new kind of number — it names the tile count.

How it works

  1. Name the unit1 cm².
  2. See the product as rows × columns (or length × breadth)The count.
  3. Then the formula has a jobNot a chant.

8Parallel lines never meet and stay equally far

Parallel sides in a rectangle stay equally far and never meet. That is why opposite sides match and why the unit-square rows are even. A pair that meets is not this rectangle’s pair.

Rails in a photo that look like they meet are an illusion, not a rectangle-test.

Figure. Parallel lines stay the same distance apart and do not meet. The two upright brackets are the same span d. The slanted dashed line is a transversal: it meets both, which is allowed. The parallels themselves never meet.

How it works

  1. Check opposite sides equal (given or constructed)The pair.
  2. Check they do not meet and the distance staysParallel as used here.
  3. Then l × b is legal for that rectangleThe figure earned the formula.
A 7 cm by 4 cm rectangle has area
  1. 28 cm²
  2. 22 cm²
  3. 11 cm²

l × b is the tile-count; 22 is the walk.

Notes

  • The official chapter title is “Area”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • rectangle area = l × b
  • square area = a × a
  • rectangle perimeter = 2(l + b)

Recap

Hold these pegs from the official chapter “Area”. The wording is ExamMaster’s teaching, not a textbook recap.

Rectangle and Squares
A rectangle’s area is length × breadth in square units.
Mark what is given on the figure
Mark what is given on the figure: ticks, lengths, a right-box, a height to a base.
A definition is a test, not a picture
Area is a test: a count of unit squares (or a taught product that equals that count).
Equal marks must be earned
Equal marks must be earned: two ticks mean those sides were given equal.
Perimeter is the walk around
Perimeter is the walk around: add the outer sides.
Area is the tiles inside
Area is the tiles inside. Gaps and overlaps are not allowed in the count. A triangle on a grid is half a rectangle when that is the taught move — name the half.

Practise Area

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  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
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