• Home
  • /
  • Blog
  • /
  • How to Construct a Rectangle Using Compass and Ruler – Methods, Steps & Examples

How to Construct a Rectangle Using Compass and Ruler – Methods, Steps & Examples

CodingHero - How to Construct a Rectangle Using Compass and Ruler - Methods, Steps & Examples Construction of Rectangle 00

This post is also available in: हिन्दी (Hindi)

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$.

construct a rectangle

Let’s understand how to construct a rectangle using compass and ruler with steps and examples.

How to Construct a Rectangle Using Compass and Ruler?

A rectangle is a quadrilateral with opposite sides of equal length and angles of the same measure of $90^{\circ}$. There are three methods of constructing a rectangle depending on the parameter known for construction. You can construct a unique rectangle if

  • length of two adjacent sides is known
  • length of a side and a diagonal is known
  • length of one diagonal and the angle between the two diagonals is known

How to Construct a Rectangle With Two Given Sides?

Since the two adjacent sides of a rectangle are perpendicular to each other and also the opposite sides are equal, therefore, you can construct a unique rectangle if the length of the adjacent sides is known.

The following are the steps to construct a unique rectangle with given two adjacent sides.

Step 1: Draw a side $\text{AB}$ of a given length

construct a rectangle

Step 2: Draw a perpendicular $\text{AE}$ to $\text{AB}$ at the point $\text{A}$

construct a rectangle

Read to know how to draw a perpendicular line.

Step 3: Draw a perpendicular $\text{BF}$ to $\text{AB}$ at the point $\text{B}$

construct a rectangle

Step 4: With the help of a compass, cut an arc of the length of the adjacent side on $\text{AE}$ at $\text{D}$

construct a rectangle

Step 5: With the help of a compass, cut an arc of the length of the adjacent side on $\text{BF}$ at $\text{C}$

construct a rectangle

Step 6: Join the points $\text{B}$ and $\text{C}$, $\text{C}$ and $\text{D}$, $\text{D}$ and $\text{A}$

construct a rectangle

$\text{ABCD}$ is a rectangle where the adjacent sides are of length $\text{AB}$ and $\text{BC}$ respectively.

Is your child struggling with Maths?
frustrated-kid
We can help!
Country
  • Afghanistan 93
  • Albania 355
  • Algeria 213
  • American Samoa 1-684
  • Andorra 376
  • Angola 244
  • Anguilla 1-264
  • Antarctica 672
  • Antigua & Barbuda 1-268
  • Argentina 54
  • Armenia 374
  • Aruba 297
  • Australia 61
  • Austria 43
  • Azerbaijan 994
  • Bahamas 1-242
  • Bahrain 973
  • Bangladesh 880
  • Barbados 1-246
  • Belarus 375
  • Belgium 32
  • Belize 501
  • Benin 229
  • Bermuda 1-441
  • Bhutan 975
  • Bolivia 591
  • Bosnia 387
  • Botswana 267
  • Bouvet Island 47
  • Brazil 55
  • British Indian Ocean Territory 246
  • British Virgin Islands 1-284
  • Brunei 673
  • Bulgaria 359
  • Burkina Faso 226
  • Burundi 257
  • Cambodia 855
  • Cameroon 237
  • Canada 1
  • Cape Verde 238
  • Caribbean Netherlands 599
  • Cayman Islands 1-345
  • Central African Republic 236
  • Chad 235
  • Chile 56
  • China 86
  • Christmas Island 61
  • Cocos (Keeling) Islands 61
  • Colombia 57
  • Comoros 269
  • Congo - Brazzaville 242
  • Congo - Kinshasa 243
  • Cook Islands 682
  • Costa Rica 506
  • Croatia 385
  • Cuba 53
  • Cyprus 357
  • Czech Republic 420
  • Denmark 45
  • Djibouti 253
  • Dominica 1-767
  • Ecuador 593
  • Egypt 20
  • El Salvador 503
  • Equatorial Guinea 240
  • Eritrea 291
  • Estonia 372
  • Ethiopia 251
  • Falkland Islands 500
  • Faroe Islands 298
  • Fiji 679
  • Finland 358
  • France 33
  • French Guiana 594
  • French Polynesia 689
  • French Southern Territories 262
  • Gabon 241
  • Gambia 220
  • Georgia 995
  • Germany 49
  • Ghana 233
  • Gibraltar 350
  • Greece 30
  • Greenland 299
  • Grenada 1-473
  • Guadeloupe 590
  • Guam 1-671
  • Guatemala 502
  • Guernsey 44
  • Guinea 224
  • Guinea-Bissau 245
  • Guyana 592
  • Haiti 509
  • Heard & McDonald Islands 672
  • Honduras 504
  • Hong Kong 852
  • Hungary 36
  • Iceland 354
  • India 91
  • Indonesia 62
  • Iran 98
  • Iraq 964
  • Ireland 353
  • Isle of Man 44
  • Israel 972
  • Italy 39
  • Jamaica 1-876
  • Japan 81
  • Jersey 44
  • Jordan 962
  • Kazakhstan 7
  • Kenya 254
  • Kiribati 686
  • Kuwait 965
  • Kyrgyzstan 996
  • Laos 856
  • Latvia 371
  • Lebanon 961
  • Lesotho 266
  • Liberia 231
  • Libya 218
  • Liechtenstein 423
  • Lithuania 370
  • Luxembourg 352
  • Macau 853
  • Macedonia 389
  • Madagascar 261
  • Malawi 265
  • Malaysia 60
  • Maldives 960
  • Mali 223
  • Malta 356
  • Marshall Islands 692
  • Martinique 596
  • Mauritania 222
  • Mauritius 230
  • Mayotte 262
  • Mexico 52
  • Micronesia 691
  • Moldova 373
  • Monaco 377
  • Mongolia 976
  • Montenegro 382
  • Montserrat 1-664
  • Morocco 212
  • Mozambique 258
  • Myanmar 95
  • Namibia 264
  • Nauru 674
  • Nepal 977
  • Netherlands 31
  • New Caledonia 687
  • New Zealand 64
  • Nicaragua 505
  • Niger 227
  • Nigeria 234
  • Niue 683
  • Norfolk Island 672
  • North Korea 850
  • Northern Mariana Islands 1-670
  • Norway 47
  • Oman 968
  • Pakistan 92
  • Palau 680
  • Palestine 970
  • Panama 507
  • Papua New Guinea 675
  • Paraguay 595
  • Peru 51
  • Philippines 63
  • Pitcairn Islands 870
  • Poland 48
  • Portugal 351
  • Puerto Rico 1
  • Qatar 974
  • Romania 40
  • Russia 7
  • Rwanda 250
  • Réunion 262
  • Samoa 685
  • San Marino 378
  • Saudi Arabia 966
  • Senegal 221
  • Serbia 381 p
  • Seychelles 248
  • Sierra Leone 232
  • Singapore 65
  • Slovakia 421
  • Slovenia 386
  • Solomon Islands 677
  • Somalia 252
  • South Africa 27
  • South Georgia & South Sandwich Islands 500
  • South Korea 82
  • South Sudan 211
  • Spain 34
  • Sri Lanka 94
  • Sudan 249
  • Suriname 597
  • Svalbard & Jan Mayen 47
  • Swaziland 268
  • Sweden 46
  • Switzerland 41
  • Syria 963
  • Sao Tome and Principe 239
  • Taiwan 886
  • Tajikistan 992
  • Tanzania 255
  • Thailand 66
  • Timor-Leste 670
  • Togo 228
  • Tokelau 690
  • Tonga 676
  • Trinidad & Tobago 1-868
  • Tunisia 216
  • Turkey 90
  • Turkmenistan 993
  • Turks & Caicos Islands 1-649
  • Tuvalu 688
  • U.S. Outlying Islands
  • U.S. Virgin Islands 1-340
  • UK 44
  • US 1
  • Uganda 256
  • Ukraine 380
  • United Arab Emirates 971
  • Uruguay 598
  • Uzbekistan 998
  • Vanuatu 678
  • Vatican City 39-06
  • Venezuela 58
  • Vietnam 84
  • Wallis & Futuna 681
  • Western Sahara 212
  • Yemen 967
  • Zambia 260
  • Zimbabwe 263
Age Of Your Child
  • Less Than 6 Years
  • 6 To 10 Years
  • 11 To 16 Years
  • Greater Than 16 Years

How to Construct a Rectangle With Given One Side and One Diagonal?

Since the two diagonals of a rectangle are equal and bisect each other, therefore, you can construct a unique rectangle if the length of the one side and diagonal is known.

The following are the steps to construct a unique rectangle with given one side and one diagonal.

Step 1: Draw a line segment $\text{AB}$ of given length

construct a rectangle

Step 2: At $\text{B}$, draw $\text{BE} \perp \text{AB}$

construct a rectangle

Step 3: With $\text{A}$ as centre and radius equal to the length of the diagonal, draw an arc cutting $\text{BE}$ at $\text{C}$

CodingHero - How to Construct a Rectangle Using Compass and Ruler - Methods, Steps & Examples Construction of Rectangle 10

Step 4: With $\text{B}$ as centre and radius equal to the length of the diagonal, draw an arc

construct a rectangle

Step 5: With $\text{C}$ centre and radius equal to the length of the side, another arc, cutting the previous arc at $\text{D}$.

construct a rectangle

Step 6: Join $\text{A}$ and $\text{D}$, $\text{C}$ and $\text{D}$

construct a rectangle

$\text{ABCD}$ is a rectangle where the side $\text{AB}$ and diagonal $\text{AC}$ of given length.

Famous Math Competitions for Kids

How to Construct a Rectangle With Given One Diagonal and the Angle Between the Diagonals?

Since the two diagonals of a rectangle are equal and bisect each other, therefore, you can construct a unique rectangle if the length of a diagonal and the angle between the diagonals are known.

The following are the steps to construct a unique rectangle with given one diagonal and the angle between the diagonals.

Step 1: Draw the diagonal $\text{AC}$ of given length

construct a rectangle

Step 2: Draw the perpendicular bisector of $\text{AC}$ and locate the mid-point $\text{O}$ of $\text{AC}$

construct a rectangle

Read to know how to draw a perpendicular bisector.

Step 3: Through $\text{O}$, construct a line $\text{POQ}$ so that $\angle \text{POC}$ equal to the angle between the diagonals

construct a rectangle

Step 4: From $\text{O}$ cut $\text{OB}$ and $\text{OD}$ equal to half the length of diagonal given

construct a rectangle

Note: $\text{O}$ is the midpoint of the diagonals $\text{AC}$ and $\text{BD}$.

Step 5: Join $\text{A}$ with $\text{B}$, $\text{B}$ with $\text{C}$, $\text{C}$ with $\text{D}$ and $\text{D}$ with $\text{A}$.

construct a rectangle

 $\text{ABCD}$ is a rectangle where the diagonal $\text{AC}$ of given length.

Practice Problems

  1. What is a rectangle in geometry?
  2. Construct a rectangle whose adjacent sides are $5 \text{cm}$ and $8 \text{cm}$.
  3. Construct a rectangle whose adjacent sides are $5 \text{cm}$ and $8 \text{cm}$.
  4. Construct a rectangle whose one side and one diagonal are of length $4 \text{cm}$ and $7 \text{cm}$ respectively.
  5. Construct a rectangle whose diagonal is of length $8 \text{cm}$ and the angle between the diagonals is $60^{\circ}$.

FAQs

What is rectangle with diagram?

construct a rectangle

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$.

What are the different methods of constructing a rectangle?

The different methods of constructing a rectangle are when
a) length of two adjacent sides is known
b) length of a side and a diagonal is known
c) length of one diagonal and the angle between the two diagonals is known

Conclusion

A rectangle is a closed 2D shape with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to $90^{\circ}$. A unique rectangle can be constructed using compass and ruler when the length of two adjacent sides, the length of a side, and a diagonal or length of one diagonal and the angle between the two diagonals is known.

Recommended Reading

{"email":"Email address invalid","url":"Website address invalid","required":"Required field missing"}
>