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Class 6 Maths: Perimeter and Area, 8 practice questions with answers

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These are 8 practice questions on Class 6 Maths Chapter 6, Perimeter and Area, of the new NCERT textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover the perimeter of a rectangle, a regular polygon and a square, why the same perimeter can enclose different areas, what happens to a square when its side doubles, finding the mistake in an area estimate on squared paper, and the area of a triangle as half a rectangle. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 6, printed pages 129 to 150):

6.1 Perimeter

Question 1. Ravi says the perimeter of a rectangle 29 cm long and 17 cm wide is 29 + 17 = 46 cm. Find his mistake and the correct perimeter.

Answer: he added only two of the four sides; the perimeter is 92 cm. A rectangle has two lengths and two breadths, so its perimeter is 2 × (length + breadth) = 2 × (29 cm + 17 cm) = 2 × 46 cm = 92 cm. Ravi's 46 cm is only half of the way round. (Perimeter of a rectangle, pages 129 and 130.)

Question 2. A regular polygon has sides 7 cm long and a perimeter of 63 cm. How many sides does it have?

Answer: 9 sides. All the sides of a regular polygon are equal, so its perimeter is the number of sides × the length of a side, just as an equilateral triangle's is 3 × a side. So the number of sides = 63 ÷ 7 = 9. Check: 9 × 7 cm = 63 cm. (Regular polygons and the perimeter of an equilateral triangle, pages 135 and 136.)

Question 3. Wire fencing all around a square vegetable patch cost ₹6,264, at ₹29 a metre. How long is each side of the patch?

Answer: 54 m. The length of wire is the cost ÷ the price of one metre = 6,264 ÷ 29 = 216 m, and this is the perimeter of the square. The perimeter of a square is 4 × a side, so each side = 216 ÷ 4 = 54 m. Check: 4 × 54 m = 216 m, and 216 × ₹29 = ₹6,264. (Perimeter of a square, page 130.)

6.2 Area

Question 4. Meera says, "Two rectangles with the same perimeter must have the same area." Test her claim with a rectangle 41 cm by 17 cm and another 39 cm by 19 cm.

Answer: she is wrong; both perimeters are 116 cm, but the areas are 697 sq cm and 741 sq cm. Perimeters: 2 × (41 + 17) = 2 × 58 = 116 cm and 2 × (39 + 19) = 2 × 58 = 116 cm, the same. Areas: 41 × 17 = 697 sq cm and 39 × 19 = 741 sq cm, different. Two figures can have the same perimeter and different areas. (Perimeter of a rectangle, page 130; area of a rectangle, page 137; summary, page 150.)

Question 5. A square has sides of 31 m. Sana says, "If I double the side, the perimeter and the area both double." Find the perimeter and the area before and after, and say where she is wrong.

Answer: the perimeter doubles (124 m to 248 m), but the area becomes four times as large (961 sq m to 3,844 sq m). Before: perimeter = 4 × 31 = 124 m and area = 31 × 31 = 961 sq m. After, with sides of 62 m: perimeter = 4 × 62 = 248 m, which is double, but area = 62 × 62 = 3,844 sq m, which is 4 × 961. Doubling the side doubles both the length and the width of the square, so the area is doubled twice. (Perimeter of a square, page 130; area of a square, pages 137 and 150.)

Question 6. Tina traces a leaf on squared paper where each square is 1 sq unit. Inside the outline she counts 31 full squares, 9 squares that are more than half covered, 6 squares that are exactly half covered and 7 squares that are less than half covered. She adds everything: 31 + 9 + 6 + 7 = 53 sq units. Find her mistake and give a better estimate of the area.

Answer: she counted every square as a whole one; the estimate is 43 sq units. The conventions for squared paper are: a full square is 1 sq unit, parts less than half a square are ignored, parts more than half count as 1 sq unit, and exactly half a square counts as ½ sq unit. So the 7 squares that are less than half covered are ignored (not counted as 7), and the 6 half squares count 6 × ½ = 3 (not 6). The estimate is 31 + 9 + 3 = 43 sq units. (Estimating area on squared paper, page 140.)

6.3 Area of a triangle

Question 7. A rectangle 34 cm long and 19 cm wide is cut along a diagonal into two triangles. Find the area of one triangle. Kabir says each triangle's perimeter is also half of the rectangle's perimeter. Is he right?

Answer: each triangle has an area of 323 sq cm; Kabir is wrong, its perimeter is more than half. The rectangle's area is 34 × 19 = 646 sq cm, and the diagonal cuts it into two equal triangles, so each has 323 sq cm. But the rectangle's perimeter is 2 × (34 + 19) = 106 cm, half of which is 53 cm, while each triangle's sides are 34 cm, 19 cm and the diagonal: its perimeter is 53 cm plus the diagonal, so it is more than 53 cm. Area halves; perimeter does not. (Area of a triangle from a rectangle, page 142; perimeter of a triangle, page 131.)

Question 8. A triangle is drawn inside a rectangle with its base along the whole 17 cm bottom side and its top corner on the top side. The triangle's area is 391 sq cm. How tall is the rectangle?

Answer: 46 cm. A triangle drawn this way has half the area of the rectangle, so the rectangle's area is 2 × 391 = 782 sq cm. Its length is 17 cm, so its height = 782 ÷ 17 = 46 cm. Check: 17 × 46 = 782, and half of 782 is 391. (A triangle with half the area of its rectangle, pages 143 and 144.)

Questions students ask

What is the perimeter of a rectangle? Twice the sum of its length and breadth: perimeter = 2 × (length + breadth). (Pages 129 and 130.)

What is the difference between perimeter and area? Perimeter is the distance around the boundary of a figure, measured in units of length such as cm or m. Area is the amount of region the figure encloses, measured in square units such as sq cm or sq m. (Pages 129, 137 and 150.)

How do you find the perimeter of a regular polygon? All its sides are equal, so multiply the length of one side by the number of sides; for an equilateral triangle that is 3 × a side, and for a square 4 × a side. (Pages 130, 135 and 136.)

How do you find the area of a triangle? In this chapter, by seeing it as half of a rectangle: a diagonal cuts a rectangle into two triangles of equal area, and a triangle with its base on one side of a rectangle and its top on the opposite side has half the rectangle's area. (Pages 142 to 144.)

How do you find the area and perimeter of a rectangle and a square? Rectangle: perimeter = 2 × (length + breadth), area = length × width. Square: perimeter = 4 × side, area = side × side. (Pages 129 to 130, 137 and 150.)

Where are the worksheets with answers? The printable Class 6 Perimeter and Area worksheet has an answer key, and the free practice set marks your answers instantly.

Which is exercise 6.1, 6.2 and 6.3? The new Ganita Prakash book has no numbered exercises. 6.1 Perimeter, 6.2 Area and 6.3 Area of a Triangle are sections, and each has "Figure it Out" practice sets. NCERT's own answers to them are printed after the chapter in the same PDF.

Is this the same as Class 9 Perimeter and Area? No. The Class 9 chapter, Measuring Space: Perimeter and Area, goes on to circles, Heron's formula and more; see the Class 9 guide.

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 128.

The facts are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.