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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Where m > 0 , a > 0 , and b > 0 , the graph of y = m x + b , and the vertical line through a ,   0 determines a trapezoidal region in Quadrant I. Find an expression for the area of this trapezoid in terms of a , b , and m .

To determine

To find:

An expression for the area of the trapezoid in terms of a, b, and m which is formed by the graph of y=mx+b (along with the x and y axes) and the vertical line through a, 0 determines in Quadrant I in which m>0, a>0 and b>0.

Explanation

Consider the line equation y=mx+b and the vertical line through a, 0.

The graph of this line equation by considering m>0, a>0 and b>0.

The trapezium ABCDE formed by the above graph has one triangle ABE and one rectangle BCDE.

Thus in order to find the area of trapezium, we can add the area of triangle and area of rectangle.

The general formula for the area of the triangle is 12(base × height).

The general formula for area of the rectangle is length × breadth.

Consider the rectangle BCDE,

Length is a.

Breadth is b.(It is a y-intercept)

Thus, area of the rectangle is ab.

Consider the triangle ABE,

Base of the triangle is determined by finding the x-intercept

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