NCERT Solutions Ganita Prakash Chapter 6 Figure it Out — Perimeter

Book page 132 Updated on2026-09-05

Q1.

Find the missing terms: a. Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?. b. Perimeter of a square = 20 cm; side of a length = ?. c. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?.

Answer

Use the two formulas backwards.

(a) Perimeter = 14 cm, breadth = 2 cm

Perimeter = 2 × (length + breadth)
14 = 2 × (length + 2)
length + 2 = 14 ÷ 2 = 7
length = 7 − 2 = 5 cm

(b) Perimeter of a square = 20 cm

Perimeter = 4 × side
20 = 4 × side
side = 20 ÷ 4 = 5 cm

(c) Perimeter = 12 m, length = 3 m

12 = 2 × (3 + breadth)
3 + breadth = 12 ÷ 2 = 6
breadth = 6 − 3 = 3 m

Note: the answer key printed at the end of the book writes “3 cm” for part (c). The measurements in the question are in metres, so the correct answer is 3 m.

Why halve first: a rectangle has two lengths and two breadths. Half the perimeter is therefore exactly one length + one breadth, so dividing by 2 straight away is the quickest first step.

Q2.

A rectangle having sidelengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?

Answer

The same piece of wire is used, so the perimeter does not change.

Length of wire = perimeter of the rectangle
= 2 × (5 cm + 3 cm) = 2 × 8 cm = 16 cm
Side of the square = 16 ÷ 4 = 4 cm

Answer: each side of the square is 4 cm.

Did you notice? The wire covers the same distance, but the region it encloses changes:
area of the rectangle = 5 × 3 = 15 sq cm, area of the square = 4 × 4 = 16 sq cm. Same perimeter, more area — the square always encloses the most.

Q3.

Find the length of the third side of a triangle having a perimeter of 55 cm and having two sides of length 20 cm and 14 cm, respectively.

Answer

Perimeter of a triangle = sum of its three sides
55 = 20 + 14 + third side
55 = 34 + third side
third side = 55 − 34 = 21 cm

Answer: the third side is 21 cm.

Check it yourself: 20 + 14 + 21 = 55 ✔

Q4.

What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m, if the fence costs ₹40 per metre?

Answer

The fence runs all around the park, so we first need the perimeter.

Perimeter = 2 × (length + breadth)
= 2 × (150 m + 120 m)
= 2 × 270 m = 540 m

Now multiply by the rate:

Cost = 540 × ₹40 = ₹21,600

Answer: the fencing will cost ₹21,600.

Why perimeter and not area: fencing, lace, tape, rope and border designs run along the boundary, so they always need the perimeter. Tiles, carpets, grass and paint cover the inside, so they need the area.

Q5.

A piece of string is 36 cm long. What will be the length of each side, if it is used to form: a. A square, b. A triangle with all sides of equal length, and c. A hexagon (a six sided closed figure) with sides of equal length?

Answer

In every case the whole string becomes the perimeter, so divide 36 cm by the number of equal sides.

Figure	Number of equal sides	Working	Length of each side
a. Square	4	36 ÷ 4	9 cm
b. Equilateral triangle	3	36 ÷ 3	12 cm
c. Regular hexagon	6	36 ÷ 6	6 cm

The rule behind all three: for a regular polygon, perimeter = number of sides × length of a side. So length of a side = perimeter ÷ number of sides.

Q6.

A farmer has a rectangular field having length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope as shown. What is the total length of rope needed?

Answer

One round of rope goes once around the field — that is one perimeter.

Perimeter of the field = 2 × (230 m + 160 m)
= 2 × 390 m = 780 m

The farmer wants 3 rounds:

Total rope = 3 × 780 m = 2340 m

Answer: 2340 m of rope is needed (that is 2 km 340 m).

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