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The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.
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.
In a triangle, any arbitrary side can be considered the base. The two endpoints of the base are called base vertices and the corresponding angles are called base angles. The third vertex opposite the base is called the apex. The extended base of a triangle (a particular case of an extended side) is the line that contains the base.
This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula , where the base is taken as side a and the height is the altitude from the vertex A (opposite side a).
An equilateral triangle is a triangle in which all three sides have the same length, ... has a height of /, the sine of 60°. The area of an equilateral ...
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
Height is normal to the plane formed by the length and width. Height is also used as a name for some more abstract definitions. These include: The height or altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side; The height of a pyramid, which is the smallest distance from the apex to the ...
This is an isosceles triangle that is acute, but less so than the equilateral triangle; its height is proportional to 5/8 of its base. [39] The Egyptian isosceles triangle was brought back into use in modern architecture by Dutch architect Hendrik Petrus Berlage. [40] Detailed view of a modified Warren truss with verticals