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NCERT Solutions Ganita Prakash Chapter 6 Figure it Out — Area

Book page 138 Updated on2026-09-05

Q1.
The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?
Answer
Area = length × width
300 = 25 × width
width = 300 ÷ 25 = 12 m

Answer: the garden is 12 m wide.

Check it yourself: 25 × 12 = 300 ✔
Q2.
What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹8 per hundred sq m?
Answer

Step 1 — the area to be tiled.

Area = 500 m × 200 m = 1,00,000 sq m

Step 2 — how many “hundreds of sq m” is that?

1,00,000 ÷ 100 = 1000 hundreds

Step 3 — the cost.

Cost = 1000 × ₹8 = ₹8000

Answer: tiling will cost ₹8000.

Careful with the rate: the rate is per hundred square metres, not per square metre. If you forget to divide by 100, the answer becomes ₹8,00,000 — a hundred times too big.
Q3.
A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m, what is the maximum number of trees that can be planted in this grove?
Answer
Area of the grove = 100 m × 50 m = 5000 sq m
Space needed by one tree = 25 sq m
Number of trees = 5000 ÷ 25 = 200

Answer: at most 200 coconut trees can be planted.

Picture it: 25 sq m is a square patch of 5 m × 5 m. Along the length you can fit 100 ÷ 5 = 20 patches and along the width 50 ÷ 5 = 10 patches — that is 20 × 10 = 200 patches. ✔
Q4.
By splitting the following figures into rectangles, find their areas (all measures are given in metres).
Answer

Figure (a) — the staircase. Slice it into four horizontal strips (shown by the dashed lines) and add.

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Figure (a) cut into four rectangles by horizontal lines. The red numbers are the areas of the strips.
Bottom strip   3 × 3 = 9
Next strip      7 × 1 = 7
Next strip      5 × 2 = 10
Top strip       2 × 1 = 2
Total = 9 + 7 + 10 + 2 = 28 sq m

Figure (b) — the arch. Here it is quicker to take the big rectangle and remove the notch.

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Figure (b) as a 5 m × 3 m rectangle with a 3 m × 2 m piece cut out of the bottom — or as one bar plus two legs.
Whole rectangle = 5 × 3 = 15 sq m
Notch removed  = 3 × 2 = 6 sq m
Area = 15 − 6 = 9 sq m

Splitting instead of subtracting gives the same answer: top bar 5 × 1 = 5, left leg 1 × 2 = 2, right leg 1 × 2 = 2, and 5 + 2 + 2 = 9 sq m ✔

Two safe methods: (i) cut the figure into rectangles and add, or (ii) draw the smallest rectangle around it and subtract the parts that are not in the figure. Choose whichever needs less work.
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