   Chapter 5.1, Problem 34E

Chapter
Section
Textbook Problem

# Use calculus to find the area of the triangle with the given vertices. ( 2 , 0 ) ,   ( 0 , 2 ) ,   ( − 1 , 1 )

To determine

To find:

The area of the triangle with the given vertices using calculus.

Explanation

1) Concept:

Formula:

The area A of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b is

A= abfx-gxdx

fx-gx=fx-gx when fxg(x)gx-fx when gxf(x)

Equation of line passing through two points (a,b) and (c,d) is given by  y-bx-a=d-bc-a

2) Given:

The vertices 2, 0,  0,2,  (-1,1)

3) Calculation:

First, find the equations of lines passing through the given vertices.

An equation of the line passing through (2, 0) and (0, 2) is

y=-x+2

An equation of the line passing through (2, 0) and (-1,1) is

y=-13x+23

And the equation of the line passing through (0, 2) and -1,1 is

y=x+2

Now, use these equations to find the area enclosed by the given vertices

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 1520, simplify the expression. 19. (3xy24x3y)2(3xy32x2)3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Draw a scatterplot for which r = 1.

Introduction To Statistics And Data Analysis 