### Home > CALC > Chapter 1 > Lesson 1.2.5 > Problem1-84

1-84.

Examine the graph of the function $f(x) = 0.5x - 2$ at right.

1. Find the area of the shaded region using geometry. (Recall that the area below the $x$-axis is considered negative.)

Find the area of each triangle separately. Recall that the area below the $x$-axis is negative. Add the negative and the positive regions together.

[Area of triangle $A$] $+$ [Area of triangle $B$]
$\frac{1}{2}(4)(f(0))+\frac{1}{2}(7-4)(f(7))$
$\frac{1}{2}(4)(-2)+\frac{1}{2}(3)(1.5)=$

$-1\frac{3}{4}$

2. Find $k$ if $A(f, 0 ≤ x ≤ k) = 10$. How did you find your solution?

[Area of triangle $A$] $+$ [Area of triangle $B$] $=10$
Simplify, and solve for $k$.