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The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.
When the triangle is obtuse and the base is chosen to be one of the sides adjacent to the obtuse angle, then the altitude dropped perpendicularly from the apex to the base intersects the extended base outside of the triangle. The area of a triangle is its half of the product of the base times the height (length of the altitude). For a triangle ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
The area formula for a triangle can be proven by cutting two copies of the triangle into pieces and rearranging them into a rectangle. In the Euclidean plane, area is defined by comparison with a square of side length , which has area 1. There are several ways to calculate the area of an arbitrary triangle.
The area of a triangle is half the area of any parallelogram on the same base and having the same altitude. The area of a rectangle is equal to the product of two adjacent sides. The area of a square is equal to the product of two of its sides (follows from 3).
A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . Letting be the semiperimeter of the triangle, = (+ +), the area is [1]
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its
The formula of the area of an equilateral triangle can be obtained by substituting the altitude formula. [7] Another way to prove the area of an equilateral triangle is by using the trigonometric function. The area of a triangle is formulated as the half product of base and height and the sine of an angle. Because all of the angles of an ...
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