The farmer also lives in the United States, and being unfamiliar with the use of SI units, still measures his plot of land in terms of feet. Because he owns some cows that he did not want frolicking freely, he fenced the piece of land and knew the exact length and width of each edge. Imagine a farmer trying to sell a piece of land that happens to be perfectly rectangular.
The Farmer and his Daughter – Unsold Land The equation for calculating the area of a rectangle is as follows: When the length and width of a rectangle are equal, the shape is a special case of a rectangle, called a square. In the case of a rectangle, the length typically refers to the longer two edges of the quadrilateral, while the width refers to the shorter of the two edges. A quadrilateral by definition is a polygon that has four edges and vertices. It is one of the simplest shapes, and calculating its area only requires that its length and width are known (or can be measured). RectangleĪ rectangle is a quadrilateral with four right angles. Provided below are equations for some of the most common simple shapes, and examples of how the area of each is calculated. The standard unit of area in the International System of Units (SI) is the square meter, or m 2. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. Thus, the total height is Acos(θ/2) + sqrt(B² - A²sin²(θ/2)).Related Surface Area Calculator | Volume CalculatorĪrea is a quantity that describes the size or extent of a two-dimensional figure or shape in a plane. 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. 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. 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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