Concept explainers
To calculate: The area and the type of the quadrilateral formed by ABCD along with its figure.
Answer to Problem 21E
The area of the quadrilateral so formed as trapezium is
Explanation of Solution
Given information:
The four vertices of the quadrilateral
Formula used:
Area of a trapezium is half into the product of the sum of its parallel sides and its height. So, if a and b are the parallel sides of the trapezium and h is its height, area of trapezium is calculated as,
Calculation:
Consider the given four vertices of the quadrilateral
Observe that all the points lie in the first quadrant of the coordinate plane, so, plot the points in first quadrant of the coordinate plane and join the vertices to form the quadrilateral as,
In the above figure, it is observed that the quadrilateral so formed has one pair of parallel sides, which is the characteristic of the trapezium, hence, the quadrilateral so formed is a trapezium.
Recall that the area of a trapezium is half into the product of the sum of its parallel sides and its height. So, if a and b are the parallel sides of the trapezium and h is its height, area of trapezium is calculated as,
Here,
Thus, area of the quadrilateral so formed as trapezium is
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning