Finding area between two parallel lines

Question

How can I compute the area between two parallel lines $y=5x+0.21$ and $y=5x+0.01$ inside a unit square, i.e. $0\leq x,y\leq1$?

Answer 1

HINT

• make a plot of the square and the lines
• find the intersection points $(0,0.21),(0,0.01)$,etc.
• note that we can obtain the area by subtracting the areas of two triangles

Answer 2

By finding the integral:$$\int_0^1\int_0^1[5x+0.01\leq y\leq 5x+0.21]dydx$$where $[P(x,y)]$ denotes the function taking value $1$ if $P(x,y)$ is true and taking value $0$ otherwise.

But it is more handsome to choose for plotting as gimusi suggests.

Answer 3

Find the area of the two triangles, and the large rectangle