• Home
• /
• Blog
• /
• Area of A Kite – Formulas, Methods & Examples

# Area of A Kite – Formulas, Methods & Examples

September 17, 2022

Table of Contents

In geometry, the area of a plane 2D shape is the region covered by the sides of it (region bounded by the perimeter) in a two-dimensional plane. Or we can say that area of any shape is the number of unit squares that can fit into it. Here a unit square refers to a square of side $1$ unit. One good example is graph paper. By counting the number of squares in a region, you can find the area of that region.

Let’s learn about the area of a kite, its formula, and its properties.

## What is the Area of a Kite?

The area of a kite can be defined as the region covered by the perimeter of a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal. The area of a kite is always expressed in terms of $units^{2}$ such as $cm^{2}$, $in^{2},$m^{2}$,$ft^{2}$etc. ### Area of a Kite Formula A kite has two unequal diagonals bisecting each other at right angles. If$d_{1}$and$d_{2}$are the lengths of the two diagonals of a kite, its area is given by the formula$A = \frac {1}{2} \times d_{1} \times d_{2}$. Is your child struggling with Maths? 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 • RÃ©union 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 ### Area of Kite Formula Derivation Using the Diagonals Consider a kite$ABCD$, such that the adjacent sides$AB = BC$and$CD = DA$. The diagonals of the kite are$AC = d_{1}$and$BD = d_{2}$. Area of kite$ABCD$= (Area of$\triangle AOD$) + (Area of$\triangle COD$) + (Area of$\triangle AOB$) + (Area of$\triangle BOC$) =$\frac {1}{2} \times AO \times DO$+$\frac {1}{2} \times DO \times CO$+$\frac {1}{2} \times AO \times BO$+$\frac {1}{2} \times BO \times CO$=$\frac {1}{2} \times DO \times \left(AO + CO \right) + \frac {1}{2} \times BO \times \left(AO + CO \right)$=$\frac {1}{2} \times DO \times AC + \frac {1}{2} \times BO \times AC$=$\frac {1}{2} \times AC \times (DO + BO) = \frac {1}{2} \times AC \times BD = \frac {1}{2} \times d_{1} \times d_{2}$### Area of a Kite Examples Ex 1: Find the area of a kite whose diagonals are of length$12 cm$and$8 cm$. The length of the first diagonal of a kite$d_{1} = 12 cm$The length of the second diagonal of a kite$d_{2} = 8 cm$Area of a kite =$\frac {1}{2} \times d_{1} \times d_{2} = \frac {1}{2} \times 12 \times 8 = 48 cm^{2}$Ex 2: The area of a kite is$120 mm^{2}$. If one of the diagonals is$16 mm$, find the length of the second diagonal. Area of a kite$A = 120 mm^{2}$Length of one diagonal of a kite$d_{1} = 16 mm$Area of a kite$A = \frac {1}{2} \times d_{1} \times d_{2} => 120 = \frac {1}{2} \times 16 \times d_{2} => 120 = 8 \times d_{2} => d_{2} = \frac {120}{8} => d_{2} = 15 mm$## Kite – A 2D Plane Figure A kite is a quadrilateral in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal. The two diagonals are unequal and intersect at right angles. The longer diagonal of a kite bisects the shorter one. ### Properties of A Kite The following are the characteristic features of a kite • A kite has two pairs of adjacent equal sides. Here,$AC = BC$and$AD = BD$• It has one pair of opposite angles (obtuse) that are equal. Here,$\angle A = \angle B$• The longer diagonal bisects the shorter one. Here, the diagonal$AB$,$AO = OB$• The shorter diagonal forms two isosceles triangles. Here, diagonal$AB$forms two isosceles triangles:$\triangle ACB$and$\triangle ADB$.$AC = BC$and$AD = BD$in two isosceles triangles • The longer diagonal forms two congruent triangles. Here, diagonal$CD$forms two congruent triangles –$\triangle CAD$and$\triangle CBD$by$SSS$criteria • The diagonals are perpendicular to each other. Here,$AB \perp CD$• The longer diagonal bisects the pair of opposite angles. Here,$\angle ACD = \angle DCB$, and$\angle ADC = \angle CDB$## Conclusion A kite is a 2D plane figure whose two pairs of adjacent equal sides. The kite has two unequal diagonals intersecting at right angles and you can find the area of a kite by multiplying half by the product of its diagonals. ## Practice Problems 1. Find the area of a kite whose diagonals are of length •$14 in$and$8 in$•$11 cm$and$9 cm$2. Find the length of a diagonal, if the area of a kite is$84 cm^{2}$and the other diagonal is of length$4 cm$. ## Recommended Reading ## FAQs ### How do you find the area of a kite? The area of a kite can be calculated using the formula Area =$\frac {1}{2} \times d_{1} \times d_{2}$, , where$d_{1}$and$d_{2}$are its diagonals. ### How do you find the diagonals of a kite? The length of one diagonal of a kite can be found using the Pythagorean theorem. The length of the other diagonal can be found by substituting the length of the first diagonal into the area of a kite formula if the area is known. ### What is the formula for the area of a kite? The area of a kite is half the product of the lengths of its diagonals. The formula for the area of a kite is given as$\frac {1}{2} \times d_{1} \times d_{2}$, where$d_{1}$and$d_{2}\$ are its diagonals.

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