Explore chapters and articles related to this topic
General introduction
Published in Adedeji B. Badiru, Handbook of Industrial and Systems Engineering, 2013
Area of profit versus area of loss. standard formula for finding the area of a triangle: Area =(1/2) (Base)(Height). Using this formula, we have the following: Area of profit region=1/2(Base)(Height)=1/2(1100-500)(100-20)=24,000square unitsArea of loss region=1/2(Base)(Height)=1/2(250-100)(20)=1500square units
A three-dimensional indoor positioning system based on visible light communication
Published in Khaled Habib, Elfed Lewis, Frontier Research and Innovation in Optoelectronics Technology and Industry, 2018
Beibei Chen, Junyi Zhang, Wei Tang, Yujun Liu, Shaohua Liu, Yong Zuo, Yitang Dai
The area of the triangle can be obtained by Heron’s formula, which is expressed as: () S=p(p−a)(p−b)(p−c)
Some inequalities in a triangle in which the length of one side and the inradius are given
Published in International Journal of Mathematical Education in Science and Technology, 2022
It may be helpful to investigate these inequalities first, using the GeoGebra applet, which can be found at www.geogebra.org/m/qgvcwuxy. The applet contains three sliders that allow to change the length of the side BC, and . The available four buttons allow to explore separately by graphs how the lengths of the other two sides of the triangle, its semiperimeter, and area change when the position () of the incircle is changed when the length of BC and are fixed. The applet gives a clear idea that the length of the side AC, the semiperimeter, and the area of the triangle increase indefinitely with increasing x, while the length of the side BC first decreases to a certain minimum value, and then also increases indefinitely.
3D pavement macrotexture parameters from close range photogrammetry
Published in International Journal of Pavement Engineering, 2021
Marcelo Medeiros Jr., Lucas Babadopulos, Renan Maia, Veronica Castelo Branco
If a given point, corresponding to a mesh vertex (C), is taken at the centre of the polygon which corresponds to the common corner of four other adjacent vertices, four facets are formed. The surface area can be approximated by the sum of each of these facets' areas ( through ). Knowing that the area of a triangle can be calculated by the cross product of the vectors that correspond to two of its sides, the area of the facet , for instance, is given by . The surface area over the polygon abcd is then given by where n is the number of vertices of the polygon. This procedure can be extended to all the facets that constitute the surface mesh, providing this way a reasonable estimate of the surface area.
A semi-analytical pulsating source incorporated with the panel method for wave-body interactions
Published in Ships and Offshore Structures, 2021
Shan Huang, Renchuan Zhu, Le Zha, Mengxiao Gu, Hui Wang
The integral of function over the quadrilateral panel can be expressed as follows: where is the Jacobian determinant. Moreover, the Jacobian matrix can be expressed as follows: From Equation (10) Thus, the following equation can be obtained. where , is the coordinate of vertice l in the parameter space . If is defined as the area of the triangle formed by vertice l−1, l and l+1 in the Cartesian coordinate system. We can obtain Thus, the Jacobian determinant can be expressed as follows: Consequently, the integral of over the quadrilateral panel can be expressed as follows: