Perimeter and Area Sums for Class 6 — Free CBSE Worksheet PDF with Answers

Perimeter and Area is one of the most practical chapters in Class 6 CBSE maths. You learn to answer real questions: How much fencing do I need for my garden? How many tiles will cover the kitchen floor? How much paint covers a wall? The new NCERT Ganita Prakash textbook (Chapter 6) introduces these concepts through hands-on activities like counting unit squares and creating shapes on dot grids.

Perimeter is the total distance around a shape, measured in linear units like cm or m. Area is the amount of surface a shape covers, measured in square units like sq. cm or sq. m. They sound similar but measure very different things — and getting the units right is half the battle.

This worksheet has 60 questions split across three levels. Level 1 covers perimeter and area of rectangles and squares, plus unit-square counting. Level 2 introduces triangles, finding missing dimensions, and word problems. Level 3 tackles composite figures, paths, and borders.

For a rectangle with length $l$ and breadth $b$: perimeter $= 2(l + b)$ and area $= l \times b$. So a rectangle $15$ cm by $9$ cm has perimeter $2(15 + 9) = 48$ cm and area $15 \times 9 = 135$ sq. cm.

For a square with side $s$: perimeter $= 4s$ and area $= s \times s = s^2$. A square of side $12$ cm has perimeter $48$ cm and area $144$ sq. cm. Notice the units carefully: perimeter is in cm, area is in sq. cm. Always include units in your final answer — examiners deduct marks otherwise.

Finding a missing side from given perimeter or area is a common Class 6 question. If a rectangle has perimeter $48$ cm and length $14$ cm, then $48 = 2(14 + b)$, so $24 = 14 + b$, giving $b = 10$ cm. Always write the formula first, then substitute.

The area of a triangle is half the base times the perpendicular height: area $= \frac{1}{2} \times \text{base} \times \text{height}$. For a triangle with base $16$ cm and height $10$ cm, area $= \frac{1}{2} \times 16 \times 10 = 80$ sq. cm.

Important: the height must be perpendicular to the chosen base. Drawing a clear figure helps you identify which line is the base and which is the height. In a right-angled triangle, the two perpendicular sides serve as base and height. In other triangles, you may need to drop an altitude from the vertex to the base.

Composite figures are made by joining simple shapes — like an L-shape (two rectangles) or a rectangle with a semicircle on top. To find the area, break the figure into simpler pieces, find the area of each, and add them up. Always label dimensions on your diagram so you do not lose track.

Path and border problems use a standard technique. Area of path $=$ area of outer shape $-$ area of inner shape. For a rectangular plot $50$ m by $30$ m with a $2$ m wide path inside along the boundary: outer area $= 50 \times 30 = 1500$ sq. m. Inner rectangle is $46$ m by $26$ m (subtract $2 \times 2 = 4$ from each dimension), so inner area $= 46 \times 26 = 1196$ sq. m. Path area $= 1500 - 1196 = 304$ sq. m.