Constructing Squares and Rectangles

Class 6 Maths · Chapter 8: Playing with Constructions · NCERT Ganita Prakash section 8.3

Learn

Farhan wants to construct a rectangle ABCD with AB = 6 cm and BC = 4 cm. A rough sketch first helps him plan: which side first, and where each corner goes.

Step 1: draw AB = 6 cm with a ruler. Step 2: at A and at B, draw lines at 90° (use a protractor or set square). Step 3: on each line, use the compass to mark 4 cm: that gives D and C. Step 4: join D and C. Check: DC should also be 6 cm.

Why the compass for Step 3? Because a compass copies the exact length again and again, without measuring each time. That's why constructions use it.

For a square with side 5 cm, the steps are the same, but every side is 5 cm. For a rectangle with perimeter 18 cm and length 5 cm, first work out the breadth: 18 ÷ 2 = 9, and 9 − 5 = 4 cm.

18 ÷ 2 − 5 = 4

Explore: construct each shape on the grid.

Construct a rectangle 6 cm by 4 cm.
Construct a square with side 5 cm.
Construct a rectangle with perimeter 18 cm and length 5 cm.

Remember

A rough sketch helps plan a construction.
To construct a rectangle: one side, right angles at both ends, mark the other side with a compass, join.

Quick check

Divit drew AB = 7 cm and 90° lines at A and B. What should he do next?

Mark the breadth on both lines with the compass
Draw a circle around A
Join A and B again
Draw a diagonal first

Answer

Mark the breadth on both lines with the compass. Next come points D and C, at the breadth along each 90° line.

Think about it

Can you construct a rectangle if you only know that its perimeter is 20 cm? Why or why not?

One answer

You can construct one, but not one particular rectangle: 9 × 1, 8 × 2, 7 × 3, 6 × 4 and 5 × 5 all have perimeter 20 cm. You need one more fact, like the length.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.