![]() The area of the kite equals 20 x 15 x sin150°, which equals 300 x sin150°, or 150 square inches. For instance, say you have a kite with two sides that are 20 and 15 inches long, with an angle of 150° between them. To do this, use the formula A = a x b x sinC, where a and b are the lengths of the sides and C is the angle between them. Triangle BED and Triangle CED are congruent. If you don’t know the lengths of the diagonals, you can find the area of the kite using the lengths of two non-congruent sides (that is, two sides that are not of the same length) and the size of the angle between them. Step 6: Area of the triangle DEC Area of the triangle BED 72 cm2. For example, if you have a kite with a diagonal of 7 inches and another diagonal of 10 inches, the area of the kite would equal (7 x 10)/2, or 35 square inches. If you know the lengths of these diagonals, you can plug them into the formula A (area) = xy/2, where x and y are the two diagonals. Thus, the total height is Acos(θ/2) + sqrt(B² - A²sin²(θ/2)).You can easily find the area of a kite if you know the lengths of the diagonals, or the two lines that connect each of the adjacent vertices (corners) of the kite. ![]() This gives the rest of the height as sqrt(B² - A²sin²(θ/2)). ![]() To find the rest of the height, we use the Pythagorean theorem with B as the hypotenuse and Asin(θ/2) as one of the legs. The partial height of the kite is Acos(θ/2). Using trigonometry, we can deduce that the total width of the kite is 2Asin(θ/2). For the sake of example, let's say the known angle is θ which is the angle formed by two shorter sides with length A. Suppose you know the side lengths of the kite and one of either the top or bottom angles. Since there are two halves, the total area is ABsin(φ). Using the SAS formula for the area of a triangle, we can see that half of the kite has an area of (1/2)ABsin(φ). Suppose the two shorter sides of the kite have length A and the two longer sides have length B, and call the angle between two unequal sides φ. The triangular regions inside the rectangle and outside of the kite can be rearranged to form another kite of equal size and shape. The kite takes up exactly 1/2 of the area of the rectangle. To see why this is so, imagine drawing a rectangle around the kite with the longer side parallel to the kite's height, the shorter side parallel to the kite's width, and the points of the kite on the rectangle's perimeter. The major diagonal length is 8 cm and the minor diagonal length is 5 cm. If we represent the two measurements by W and H respectively, then the area of the kite is (1/2)WH. The width of a kite is the shorter distance between opposite points and the height is the greater distance between the other pair of opposite points. ![]() Each formula is explained below and references the diagram below the calculator on the left. For triangle 1, in centimeters, thats 36 x 21.6 / 2 388.8 square centimeters. The area of each triangle is its width times its height, divided by two. There are several formulas for computing the area of a kite depending on which measurements are known. From the diagram, you can see that the template shape contains three triangles. (If equal sides are opposite to one another, the figure is a parallelogram.) In a kite, the sides of equal length are adjacent to one another. Kite Area Calculator Fill in either WH, ABθ, ABφ, or ABλ W =Ī kite is a quadrilateral with two pairs of sides that have equal length.
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