**Question 1: Draw the following.**

**1. The square READ with RE = 5.1 cm.**

**2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.**

**3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.**

**4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?**

**Solution:**

**1. The square READ with RE = 5.1 cm.**

Steps of construction:

**Step 1:** Draw one side of the square RE = 5.1 cm.

**Step 2:** From E draw an angle of 90°.

**Step 3:** From E cut EA of 5.1 cm.

**Step 4:** Now draw an arc of 5.1 cm from both A and R, intersect them and mark the intersection point as D.

**Step 5:** Join RD and ED.

Thus, we have the required square READ.

**2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.**

Steps of construction:

Let the rhombus be ABCD with diagonals, AC = 5.2 cm and BD = 6.4 cm.

**Step 1:** Draw a line AC of 5.2 cm

**Step 2:** Draw perpendicular bisector of AC and mark the bisector point as O

**Step 3:** Draw two arcs with centre O of radius 1/2 × BD = 1/2 × 6.4 cm = 3.2 cm and these arcs will meet the bisector at point B and D

**Step 4: **Join AB, BC, CD and AD.

Hence, we have the required rhombus ABCD.

**3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.**

Steps of construction:

**Step 1:** Let the rectangle be CODE with adjacent sides CO = 5 cm and OD = 4 cm.

**Step 2:** Draw CO = 5 cm.

**Step 3: **From O draw an angle of 90°.

**Step 4:** From O cut OD = 4 cm.

**Step 5:** From C draw an arc of 4 cm and from D draw an arc of 5 cm, intersect both the arcs and mark the point as E.

**Step 6:** Join CE and DE.

Thus, we have the required rectangle CODE.

**4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?**

Steps of construction:

**Step 1: **Draw a line OK of 5.5 cm.

**Step 2:** Draw a ray at K at any convenient angle, let the angle be 60°.

**Step 3:** Now cut the ray at 4.2 cm and mark the point as A.

**Step 4: **From A draw an arc of 5.5 cm and from O draw an arc of 4.2 cm, intersect both the arcs at Y.

**Step 5:** Join OY and AY.

Thus, we have the required parallelogram OKAY.

No, it is not unique as angle K can be any angle.