Practice Questions: Playing with Constructions | Mathematics for Class 6 PDF Download

Q1: Using only a compass, draw a circle of radius 5.5 cm. Mark its center as point O.
Sol:

1. Place the compass at a fixed point O.
2. Open the compass to 5.5 cm using a ruler.
3. Draw a full circle. This is the required circle of radius 5.5 cm.

Q2: What is the definition of a radius? Give an example using a circle.

Sol: A radius is the distance from the center of a circle to any point on its boundary.
Example: In a circle with center M and point A on the circle, MA is the radius.

Q3: Draw a square with side 4.5 cm using only a ruler and compass.

Sol: 

• Draw base AB = 4.5 cm.

• Construct 90° angles at A and B.

• Using a ruler, mark point D on the perpendicular line such that AB = 4.5 cm.

You can also use a compass to measure AD.

• Draw a perpendicular line to line segment AB at point B.
• If using a compass, the next point can be easily marked with it.
• Complete the square by ensuring all sides are equal.

Q4: What are the properties of a rectangle?
Sol:

• Opposite sides are equal and parallel.
• All four angles are 90°.
• Diagonals are equal and bisect each other.

Q5: Construct a rectangle PQRS such that PQ = 6 cm and QR = 4 cm.
Sol:

• Draw PQ = 6 cm.
• Construct perpendiculars at P and Q using a compass.
• Mark S on the perpendicular at P such that PS = 4 cm.
• Mark R on the perpendicular at Q such that QR = 4 cm.
• Join S to R, ensuring SR is parallel to PQ by using the compass to maintain equal lengths.

Same process can be done as in Q3 we did.

Q6: Construct a perpendicular bisector of a line segment AB = 7 cm.
Sol:

1. Draw AB = 7 cm.
2. With compass on A and B, draw arcs above and below AB using radius > 3.5 cm. ( Choose a radius greater than half of AB (3.5 cm) to ensure the arcs intersect above and below the line.)
3. Connect arc intersections. This line is the perpendicular bisector.

Q7: In a square WXYZ, if WX = 6 cm, what is the length of diagonal WZ?
Sol:
Diagonal = side × √2 = 6 × √2 ≈ 6 × 1.41 = 8.46 cm

Q8: Construct a right angle using only compass and ruler.
Sol:

1. Draw line AB.
2. Place the compass at B, draw an arc intersecting AB at P.
3. From P, draw an arc with the same radius.
4. From B, draw another arc with a slightly larger radius to intersect the previous arc at Q.
5. Join B to Q to form a 90° angle.

Diagram draw on your own by following the above given steps.

Q9: A photo frame is square-shaped with a side of 12 cm. What is the length of its diagonal?
Sol: Diagonal = 12 × √2 ≈ 16.97 cm.

Q10: Draw a circle of diameter 8 cm. What is its radius?
Sol: Radius = Diameter ÷ 2 = 4 cm.

Draw the circle with radius 4 cm.