The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?
The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?
Show Hint
To calculate the area of a quadrilateral in 3D space, divide it into two triangles, compute the cross products of their vectors, and sum the areas.
Correct Answer: 24
Solution and Explanation
\(=\frac{1}{2}[6+30-42-2-10-42+6+6]\)
\(=\frac{1}{2}[48]\)
\(=24\)
The correct answer is 24.
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Concepts Used:
Coordinates of a Point in Space
Three-dimensional space is also named 3-space or tri-dimensional space.
It is a geometric setting that carries three values needed to set the position of an element. In Mathematics and Physics, a sequence of ‘n’ numbers can be acknowledged as a location in ‘n-dimensional space’. When n = 3 it is named a three-dimensional Euclidean space.
The Distance Formula Between the Two Points in Three Dimension is as follows;
The distance between two points P1 and P2 are (x1, y1) and (x2, y2) respectively in the XY-plane is expressed by the distance formula,
Read More: Coordinates of a Point in Three Dimensions