Suppose CB = 8 cm, AB = 15 cm, and angle B is 90 degrees. The total area is found by adding the areas of the two triangles.Īrea of the kite = area of triangle ABC + area of triangle ADCĪrea of the kite = 1/2 + 1/2Īrea of the kite = (1/2 + 1/2)Īrea of the kite = (1) Therefore, the area of triangle ADC is equal to the area of triangle ABC. Since diagonal d 1 is a line of symmetry, triangle ADC and triangle ABC are congruent triangles. This concept is based on finding the area of a triangle given sas (side-angle-side).įor example, looking at the figure above, two unequal sides could be CB and AB. Thus, the total height is Acos(θ/2) + sqrt(B² - A²sin²(θ/2)).If the unequal sides of a kite are known along with the included angle, the area of a kite is the product of the unequal sides and the sine of the included angle.Īrea of the kite above = CB × AB × sin(B) b) /2, so the area of CDB is z·y/2, and the area of ADB is (x. The area of a triangle is given by the formula Area (h Lets call the lengths of OC z, then since ACx, the length of OA is x-z. So OC is the height of triangle CDB, and OA is the height of triangle ADB. This gives the rest of the height as sqrt(B² - A²sin²(θ/2)). We know the diagonals of a kite are perpendicular to each other. 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. If we know the diagonals of a kite, we can use the diagonals formula to find. 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. Kite Area Formula A kite is a quadrilateral with two pairs of equal-length sides. 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. There are several formulas for computing the area of a kite depending on which measurements are known. (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. Given: Kite ROPE E OE)(PR) Prove: Area of kite ROPE Proof: Statements Reasons KITE. 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. The area of a kite is half the product of the lengths of its diagonals.
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