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Sign up. Thank you! There are many equations for calculating the area of a triangle based on what information is available. 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.
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.
The formula is as follows:. At this point in time, through extreme effort and perseverance, the farmer has finally sold his 21, sq ft plot of land and has decided to use some of the money earned to build a pool for his family.
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.
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.
Being a doting father, the farmer acquiesces to his daughter's request and proceeds to plan the construction of his triangular pool. The farmer must now determine whether he has sufficient area in his backyard to house a pool. 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.
Given these dimensions, the farmer determines the necessary area as follows:. Since the longest distance between any two points of an equilateral triangle is the length of the edge of the triangle, the farmer reserves the edges of the pool for swimming "laps" in his triangular pool with a maximum length approximately half that of an Olympic pool, but with double the area — all under the watchful eyes of the presiding queen of the pool, his daughter, and the disapproving glare of his wife.
A trapezoid is a simple convex quadrilateral that has at least one pair of parallel sides. In a trapezoid, the parallel sides are referred to as the bases of the trapezoid, and the other two sides are called the legs. There exist more distinctions and classifications for different types of trapezoids, but their areas are still calculated in the same manner using the following equation:.
Two years have passed since the farmer's pool was completed, and his daughter has grown and matured. While her love for triangles still persists, she eventually came to the realization that no matter how well-"triangled" she was, triangles alone cannot make the world go round, and that Santa's workshop could not plausibly balance on the North Pole, were the world a pyramid rather than a sphere.
Slowly, she has begun to accept other shapes into her life and pursues her myriad different interests — currently freestyle BMX. As such, she requires a ramp, but unfortunately for the farmer, not just any ramp. The ramp must be comprised of only shapes that can be formed using multiple triangles, since, like her rap idol B.
B, the farmer's daughter still has difficulty accepting the reality of curved surfaces. It must, of course, also only use the number 9 in its measurements to reflect her age. The farmer decides that his best option is to build a ramp comprised of multiple rectangles, with the side face of the ramp being in the shape of a trapezoid. As the farmer has now become more comfortable with SI, he is able to be more creative with his use of units, and can build a more reasonably sized ramp while adhering to his daughter's demands.
He decides to build a ramp with a trapezoidal face with a height of 9 ft, a bottom base of length The area of the trapezoid is calculated as follows:. A circle is a simple closed shape formed by the set of all points in a plane that are a given distance from a given center point. This distance from the center to any point on the circle is called the radius. The equation for calculating the area of a circle is as follows:.
Another six years have passed, and his daughter has grown into a strong, beautiful, powerful, confident year-old ingrate solely focused on seeking external validation from acquaintances and strangers on social media while wholeheartedly ignoring genuine support from immediate family and friends. Having had an argument with her father about her excessive use of social media, she decides to prey on her father's fear of the unknown, and belief in the supernatural in order to prank him.
Not knowing where to start, she walks around town talking to a variety of strangers all of whom seemingly have endless founts of wisdom and advice, where she learns about crop circles and their association with aliens and unidentified flying objects as well as many other topics that ignore all scientific and logical explanations.
Having finally been convinced of the spherical nature of the Earth, deleted all her past social media posts relating to B. B, and expanded her love of triangles to an acceptance of other shapes, she decides to make a basic crop circle consisting of a number of concentric circles, and wants to determine the area necessary to create a crop circle with an outer radius of 15 ft.
She does so using the following equation:. Unfortunately for the farmer, not only is he terrified of the crop circle that appeared overnight on the night that his daughter told him she was at a slumber party with her friends, that for some odd reason did not result in superfluous Instagram posts he was of course his daughter's first follower , but the number of "circle investigators" and "cereologists" showing up on his farm to examine, and subsequently confirm the authenticity of the crop circle as an alien construction, cost him significant damages to his crops.
A sector of a circle is essentially a proportion of the circle that is enclosed by two radii and an arc. The farmer and his family are facing their most significant dilemma to date. One year has passed, and the farmer's daughter is now 16 years old and as part of her birthday celebration, her mother baked her favorite dessert, blackberry pie. Initially, the pie would easily have been split between three people and one raccoon, but now, half the pie has to be divided between three people as a chagrined, but satiated Platypus watches from a distance.
As a result of Platypus' inconsideration, each person gets one-third less pie, and the daughter contemplatively recalls American history class, where she learned about the Battle of the Alamo and the portrayal of the folk hero Davy Crockett and his coonskin hat.
An ellipse is the generalized form of a circle, and is a curve in a plane where the sum of the distances from any point on the curve to each of its two focal points is constant, as shown in the figure below, where P is any point on the ellipse, and F 1 and F 2 are the two foci. The semi-major axis of an ellipse, as shown in the figure that is part of the calculator, is the longest radius of the ellipse, while the semi-minor axis is the shortest.
The major and minor axes refer to the diameters rather than radii of the ellipse. The equation for calculating the area of an ellipse is similar to that for calculating the area of a circle, with the only difference being the use of two radii, rather than one since the foci are in the same location for a circle :.
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