While the farmer has begun to learn more about SI units, he is as yet uncomfortable with their use and decides that his only viable option is to construct a pool in the form of an equilateral triangle with sides 77 ft in length, since any other variation would either be too large or small. The farmer must now determine whether he has sufficient area in his backyard to house a pool. Being a doting father, the farmer acquiesces to his daughter's request and proceeds to plan the construction of his triangular pool.  Even more unfortunately for the farmer, his 7-year-old daughter who has recently traveled to Egypt vicariously through Dora the Explorer, has fallen in love with triangles, and insists that the pool not only be triangular in shape, but also that the measurements must only include the number 7, to represent her age and immortalize this point of her life in the form of a triangular pool. Unfortunately for the farmer, he does not consider the fact that the maintenance costs of a pool for one year alone could likely pay for his children to visit any pool or water theme park for years to come. The Farmer and his Daughter - Triangle DazeĪt this point in time, through extreme effort and perseverance, the farmer has finally sold his 21,780 sq ft plot of land and has decided to use some of the money earned to build a pool for his family. Briefly, the equation used in the calculator provided above is known as Heron's formula (sometimes called Hero's formula), referring to the Hero of Alexandria, a Greek mathematician and engineer considered by some to be the greatest experimenter of ancient times. As mentioned in the calculator above, please use the Triangle Calculator for further details and equations for calculating the area of a triangle, as well as determining the sides of a triangle using whatever information is available. There are many equations for calculating the area of a triangle based on what information is available. Unfortunately for the farmer, he lives in an area predominated by foreign investors with smaller feet, who felt that they should be getting more square feet for their money, and his land remains unsold today. The farmer's plot of land, which has an area of 21,780 square feet, equates to half an acre, where an acre is defined as the area of 1 chain by 1 furlong, which is defined by something else, and so on, and is why SI now exists. Tangent aside, the farmer's plot of land has a length of 220 feet, and a width of 99 feet. The foot was defined to be exactly 0.3048 meters in 1959 after having changed over an extensive period of time, as historically, the human body was often used to provide a basis for units of length, and unsurprisingly, was inconsistent based on time and location.  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.  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.

Area of rectangle formula

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