![]() SolutionĪll images/mathematical drawings were created with GeoGebra.The area of a plane figure is a measure of the amount of space inside it. To cross the field, find the length one has to traverse. The area of a kite-shaped field is 60 cm² and the length of one of its diagonal is 6cm. SolutionĪs stated above that the area of the kite is given as 1/2 ×( d1 × d2), therefore: Solved Examples of Problems With Kite-shaped Objects Exampleįind the area of a kite having diagonal lengths of 50 cm and 45 cm. This resemblance can also be seen as an example of polar exchange, a technique for finding connected points with lines and vice versa for a fixed circle. From any kite, the carved circle is tangent to its 4 sides at the 4 corners of a trapezoid that is isosceles. Kites and isosceles trapezoids can seem to be dual to each other, implying a resemblance between them that inverts the dimension of their parts, carrying vertices to sides and sides to vertices. Most of the time, there exist two sets of congruent sides in a Kite that are not congruent, such a Kite is a rhombus that represents a special case of Kite geometry. Four vertices of this kind of Kite lie at the three corners and another one at the side midpoints of the Reuleaux triangle. The right Kite is shown in Figure 3.įigure 3: The Concept of the Right Kite Equidiagonal KiteĬompared with all types of quadrilaterals, the form that has the largest proportion of its circumference to its dia is known as an equidiagonal Kite with certain angles. These Kites are cyclic quadrilaterals, i.e., there is a circle that crosses all their vertices. The right kites are the Kites that have two opposite right angles. For example, A dart or an arrowhead is a concave Kite. The small diagonal divides the Kite into two isosceles triangles.Ĭonvex: The Kite is called convex when all of its interior angles are less than 180$^$.A Kite is symmetrical about its large diagonal.The large diagonal of the Kite bisects the other diagonal.The Kite has two diagonals that cross each other at right angles.The two angles of the Kite where the unequal sides meet are same. ![]() the right kites, having two opposite right angles the rhombi, which consist of two diagonal axes of symmetry and the squares type of Kites, which are also special forms of Kite.įollowing are some properties of Kite listed point-wise. When a Kite is of convex type, the sides of the Kite are tangent to an inscribed circle. The types of Kites are described in the next sections. The diagonals of every Kite are at right angles. The smallest diagonal splits the Kite into two isosceles triangles. The Kite can be viewed as a set of congruent triangles having a standard base. Angles opposing the major diagonal in a Kite are of the same length. Kite has two diagonals that cross one another at right angles and is symmetrical around its major diagonal. Diagonal WY is the perpendicular bisector of diagonal XZ. Therefore, diagonals WY and XZ are perpendicular. Based on this, we know that the line segment from W and Y to the midpoint of XZ is the height of $\triangle$WXZ and $\triangle$CBD. Therefore, $\triangle$XYZ and $\triangle$YXZ are isosceles triangles that share a base, XZ. Diagonals of a KiteĪ kite has two diagonals that are perpendicular to each other:įor kite WXYZ as shown in Figure 2, XW $\cong$ ZW and XY $\cong$ ZY. The angles subtended by the neighboring sides that are not congruent for the kite are always congruent. = 52 cm Sides, Angles, and Diagonals of Kite Sides of a kiteĪ Kite has two sets of sides that are congruent and the congruent pair of Kite sides are not opposing faces. From the above formula, substituting x = 10 cm and y = 16 cm gives us: Where x and y are the lengths of the kite’s sides.įor example, suppose you want to find the perimeter of a kite whose side lengths are 10 and 16 cm. The formula for the perimeter for Kite is given by: Perimeter is the total distance covered while traveling along the sides of the Kite. Suppose the diagonals are 12 m and 16 m in length the kite area using the above formula, with d1 = 12 cm and d2 = 16 cm, turns out to be: ![]() Where the variables d1 and d2 represent the length of diagonals. The area represents the space enclosed by the Kite. The angles are equal where the pairs meet.
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