BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.8, Problem 21E
To determine

To calculate: The area and the type of the quadrilateral formed by ABCD along with its figure.

Expert Solution

Answer to Problem 21E

The area of the quadrilateral so formed as trapezium is 9 sq. units and its figure is,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 21E , additional homework tip  1

Explanation of Solution

Given information:

The four vertices of the quadrilateral A(1,0),B(5,0),C(4,3) and D(2,3) .

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,

  A=12(a+b)h

Calculation:

Consider the given four vertices of the quadrilateral A(1,0),B(5,0),C(4,3) and D(2,3) .

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,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 21E , additional homework tip  2

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,

  A=12(a+b)h

Here, a=2,b=4 and h=3 , so, area of the trapezium so formed will be calculated as,

  A=12(a+b)h=12(2+4)3=1263=9 sq. units

Thus, area of the quadrilateral so formed as trapezium is 9 sq. units and its figure is,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 21E , additional homework tip  3

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