In-text — Areas in Real Life — Area

1. 12 marksGanita Prakash Cl-8 Part 2, Section 7.1, page 170

   What is the area of an A4 sheet, whose sidelengths are 21 cm and 29.7 cm? Roughly how many A4 sheets would cover a school tabletop?

   Hint. It is a rectangle — but keep track of the decimal.

   Area of A4 = 21 × 29.7 = 623.7 cm²

   That is a little over 600 cm², which is worth remembering as a mental yardstick: roughly a 25 cm square.

   Covering a tabletop. A typical school desk is about 120 cm by 60 cm, so its area is 120 × 60 = 7200 cm². Dividing,

   7200 ÷ 623.7 ≈ 11.5

   so about 11 or 12 A4 sheets would cover it. Laying them out physically gives 12 sheets in a 4 × 3 arrangement (4 × 29.7 = 118.8 cm along the length, 3 × 21 = 63 cm across) — close enough to confirm the arithmetic, and a reminder that the packing answer can differ slightly from the area answer when the pieces cannot be cut.

   ✦ Answer: 623.7 cm², so roughly 12 sheets cover a 120 cm × 60 cm desk.

2. 22 marksGanita Prakash Cl-8 Part 2, Section 7.1, page 170

   Given 1 in = 2.54 cm, express 5 in and 7.4 in in centimetres, and express 5.08 cm and 11.43 cm in inches.

   Hint. Multiply to go from inches to centimetres; divide to come back.

   Inches to centimetres — multiply by 2.54.

   5 in = 5 × 2.54 = 12.7 cm 7.4 in = 7.4 × 2.54 = 18.796 cm (about 18.8 cm)

   Centimetres to inches — divide by 2.54.

   5.08 cm = 5.08 ÷ 2.54 = 2 in 11.43 cm = 11.43 ÷ 2.54 = 4.5 in

   Checking the direction. An inch is bigger than a centimetre, so a length has more centimetres than inches — 5 in became 12.7 cm, which grew, and 11.43 cm became 4.5 in, which shrank. If a conversion ever moves the wrong way, you have multiplied where you should have divided.

   ✦ Answer: 12.7 cm, 18.796 cm, 2 in, 4.5 in.

3. 33 marksGanita Prakash Cl-8 Part 2, Section 7.1, pages 170-171

   How many cm² is 1 in²? How many cm² is 10 in²? Convert 161.29 cm² to in².

   Hint. An area conversion squares the length conversion — it does not copy it.

   One square inch. A square of side 1 in is a square of side 2.54 cm, so

   1 in² = 2.54 × 2.54 = 2.54² = 6.4516 cm²

   Note that this is not 2.54 — the conversion factor gets squared because both the length and the width are converted.

   Ten square inches.

   10 in² = 10 × 6.4516 = 64.516 cm²

   Going back. Every 6.4516 cm² makes up one square inch, so divide:

   161.29 cm² = 161.29 ÷ 6.4516 = 25 in²

   The tidy answer is a good sign: 25 in² is a 5 in × 5 in square, and 5 in = 12.7 cm, so its area is 12.7 × 12.7 = 161.29 cm² ✓

   ✦ Answer: 1 in² = 6.4516 cm², 10 in² = 64.516 cm², and 161.29 cm² = 25 in².

4. 42 marksGanita Prakash Cl-8 Part 2, Section 7.1, page 171

   How many in² is 1 ft²? How many m² is 1 km²?

   Hint. Square the length conversion in each case.

   Square feet to square inches. Since 1 ft = 12 in,

   1 ft² = 12 × 12 = 144 in²

   Square kilometres to square metres. Since 1 km = 1000 m,

   1 km² = 1000 × 1000 = 1,000,000 m² (one million)

   The pattern. Whenever lengths are multiplied by k, areas are multiplied by k². Twelve becomes 144; a thousand becomes a million. This is the same fact that made doubling a square's side multiply its area by four, back on page 152.

   A caution. A common slip is to write 1 km² = 1000 m². That is out by a factor of a thousand — a square kilometre is a square of side 1000 m, which obviously holds far more than a thousand square metres.

   ✦ Answer: 1 ft² = 144 in² and 1 km² = 1,000,000 m².

5. 53 marksGanita Prakash Cl-8 Part 2, Section 7.1, page 171

   Estimate the area of your classroom and of your school, and say how many times bigger your school is than your classroom. What is an acre, and what local units of area are used in India?

   Hint. Estimate by pacing: one ordinary step is close to 0.75 m.

   Estimating a classroom. Pace out the two sides. A typical classroom is about 8 m by 6 m, so

   classroom ≈ 8 × 6 = 48 m²

   In the units furniture is sold in, that is 48 × (about 10.76) ≈ 517 ft², since 1 m ≈ 3.28 ft and so 1 m² ≈ 10.76 ft².

   Estimating a school. Treat the site as a rectangle and pace its boundary. A school occupying, say, 90 m by 60 m has

   school ≈ 90 × 60 = 5400 m²

   5400 ÷ 48 ≈ 112 times the classroom

   Your own numbers will differ — the method is what matters. Pace, multiply, and compare with the actual figure if the school office has it.

   Acres. Larger plots are sold in acres, with

   1 acre = 43,560 ft² ≈ 4047 m²

   so the 5400 m² school above is about 1.33 acres.

   Local units. Different parts of India use their own: bigha, gaj, katha, dhur, cent, ankanam and others. Their sizes are not standard — a bigha in one state is not a bigha in the next — so a local land record has to state which definition it uses. Find out which unit your own region uses and what it equals in m².

   ✦ Answer: measure by pacing and multiply — e.g. classroom ≈ 48 m², school ≈ 5400 m², so the school is about 112 times bigger; 1 acre = 43,560 ft² ≈ 4047 m², and local units include bigha, gaj, katha, dhur, cent and ankanam.

6. 63 marksGanita Prakash Cl-8 Part 2, Section 7.1, page 171

   Estimate the area of your town or city, and find the city with the largest and the smallest area in (i) India and (ii) the world. How would you compare two such figures fairly?

   Hint. Before comparing any two city areas, ask what boundary each number is measuring.

   Estimating your own town. Take its extent on a map, treat it as a rectangle or a few rectangles, and multiply. A town spanning roughly 6 km by 4 km covers about 24 km², which is 24,000,000 m² — about 4400 times the 5400 m² school of the previous question.

   The looking-up part, and why it needs care. "The city with the largest area" has no single answer until you say which boundary you mean, and the three usual choices give very different numbers:

   Boundary used	What it covers
   Municipal / city corporation limits	only the area the city government administers
   Metropolitan or urban agglomeration	the built-up spread, including suburbs beyond the limits
   Administrative district	may include large stretches of farmland and forest

   A city can therefore top one list and rank low on another. These figures also change whenever boundaries are redrawn, so look them up in a current official source — the Census of India or your state's municipal records — rather than memorising a number.

   How to compare fairly. Use the same kind of boundary for both cities, note the year, and convert both to the same unit (km²). Only then is the comparison meaningful.

   ✦ Answer: estimate by rectangles from a map (a 6 km × 4 km town ≈ 24 km²); for the largest and smallest cities, look up current official figures and state which boundary definition you used, since municipal, metropolitan and district areas give quite different rankings.

Solutions written by the tuition.in editorial team and checked against NCERT Ganita Prakash Grade 8 Part 2 (hegp207.pdf), Chapter 7 'Area', pages 148-171. HAND-WRITTEN throughout. Part 2 books carry NO printed answer key, so every answer was derived from first principles and independently recomputed in Python. FIGURES READ OFF HIGH-DPI RENDERS AND RE-SOLVED: the p.150 pinwheel, whose four rectangles all turn out to have a side of 7 in (areas 14, 21, 28, 35), giving the missing width 2 in; the p.150 step figure, where the BOLD outline encloses the dotted region together with the region below it - 50 sq m in all - so the widths are 29/4 = 7.25 m and 11/4 = 2.75 m (summing to exactly 10 m) and the missing height is (50-29)/7.25 = 84/29 = 2.90 m, which matches the 2.74 m measured off the printed drawing; the p.152 spiral tube, whose nine arms total 120 and whose eight corners are each double-counted once, giving 112 sq units - confirmed by rasterising the nine arms at 20 cells per unit and counting - with the hint's L-tube (arms 5 and 5) coming to 5+5-1 = 9; the p.152 square whose regions are s^2/4, s^2/4 and s^2/2, so doubling the side raises each by 3 times its own area; the p.157 triangles, whose '4 cm' label is centred on BC (not EC) giving areas 6, 8 and 6 sq cm; the p.158 obtuse triangle giving BY = 3 units; the p.158 three-square figure, where the line from D to H crosses the top of the first square at its midpoint, making the red region exactly s^2 and the blue exactly s^2/4, hence 12.25 sq units and 144 sq units; the p.160 quadrilateral (66 sq cm) and shaded region (180-30-40 = 110 sq cm); the p.160 blue 'bowtie', whose two triangles share the full width and whose heights sum to the rectangle's, so it is exactly half - measured as 0.4987 of the printed rectangle; the seven p.162 parallelograms, measured by connected-component analysis to have identical filled areas to within 0.02% (all base 5, height 3, area 15) with leans of 0.4, 1.2, 2.5, 0.6, 0.9, 2.0 and 2.8 grid units, so (g) has the maximum perimeter and (a) the minimum; the p.163 parallelograms (28, 15, 24 and 8.8 sq cm) and QN = 72/7.6 = 180/19 = 9.47 cm; the p.169 trapezia (136 sq ft, 420 sq m, 100 sq in and 120 sq ft); the p.170 hexagon, whose long diagonal and radius cut it into 3, 1 and 2 of the six unit equilateral triangles, giving the ratio 3:1:2; and the p.170 trapezium ZYXW, where ASA gives triangle ZYA congruent to triangle BXA. Unit work checked: A4 = 21 x 29.7 = 623.7 sq cm; 1 sq in = 2.54^2 = 6.4516 sq cm; 161.29 / 6.4516 = 25 sq in exactly; 5 in = 12.7 cm; 7.4 in = 18.796 cm; 5.08 cm = 2 in; 11.43 cm = 4.5 in; 1 sq ft = 144 sq in; 1 sq km = 1,000,000 sq m; 1 acre = 43,560 sq ft.. Questions are referenced from the NCERT textbook for identification.