NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.1 – Practical Geometry, has been designed by the NCERT to test the knowledge of the student on the topic – Constructing a Quadrilateral – When the lengths of four sides and a diagonal are given

### NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.1 – Practical Geometry

**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.1 – Practical Geometry**

**1. Construct the following quadrilaterals**

**i. Quadrilateral ABCD**

**AB = 4.5 cm**

**BC = 5.5 cm**

**CD = 4 cm**

**AD = 6 cm**

**AC = 7 cm**

**Solution:**

**Steps for construction of a Quadrilateral**

- Step 1. Draw the diagonal AC = 7 cm
- Step 2. With A as centre and radius 4.5 cm (= AB), draw an arc on one side of AC
- Step 3. With C as centre and radius 5.5 cm (= BC), draw an arc intersecting the previous arc at point B
- Step 4. With A as centre and radius 6 cm (= AD), draw an arc on other side of AC
- Step 5. With C as centre and radius 4 cm (= CD), draw an arc intersecting the previous arc at point D
- Step 6. Join AB, BC, AD and CD

ABCD is the required quadrilateral.

**ii. Quadrilateral JUMP**

**JU = 3.5 cm**

**UM = 4 cm**

**MP = 5 cm**

**PJ = 4.5 cm**

**PU = 6.5 cm**

**Solution:**

**Steps for construction of a Quadrilateral**

**Step 1.**Draw the diagonal PU = 6.5 cm**Step 2.**With P as centre and radius 5 cm (= MP), draw an arc on one side of PU**Step 3.**With U as centre and radius 4 cm (= UM), draw an arc intersecting the previous arc at point M**Step 4.**With P as centre and radius 4.5 cm (= PJ), draw an arc on other side of PU**Step 5.**With U as centre and radius 3.5 cm (= JU), draw an arc intersecting the previous arc at point J**Step 6.**Join JU, UM, MP and PJ

JUMP is the required quadrilateral.

**iii. Parallelogram MORE**

**OR = 6 cm **

**RE = 4.5 cm**

**EO = 7.5 cm**

**Solution:**

ME = OR = 6 cm (Opposite sides of a parallelogram are equal)

MO = RE = 4.5 cm

**Steps for construction of a Parellelogram**

- Step 1. Draw the diagonal EO = 7.5 cm
- Step 2. With E as centre and radius 6 cm (= ME), draw an arc on one side of EO
- Step 3. With O as centre and radius 4.5 cm (= MO), draw an arc intersecting the previous arc at point M
- Step 4. With E as centre and radius 4.5 cm (= RE), draw an arc on other side of EO
- Step 5. With O as centre and radius 6 cm (= OR), draw an arc intersecting the previous arc at point R
- Step 6. Join MO, OR, RE and EM

MORE is the required parallelogram.

**iv. Rhombus BEST**

**BE = 4.5 cm**

**ET = 6 cm**

**Solution:**

BE = ES = ST = TB = 5 cm (All sides of a rhombus are equal)

**Steps for construction of a Rhombus**

- Step 1. Draw the diagonal ET = 6 cm
- Step 2. With E as centre and radius 4.5 cm (= BE = ES), draw an arc on both sides of ET
- Step 3. With T as centre and radius 4.5 cm (= ST = TB), draw an arc intersecting the previous arcs at point B and S
- Step 4. Join BE, ES, ST and TB

BEST is the required rhombus.

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2 – Practical Geometry can be accessed by clicking here**

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