Answer
$\frac{7}{16}$
Work Step by Step
$60 \times 60=3600$
(The probability that you and your friend meet is equal to the probability that a point chosen at random on the graph falls in the area where you meet. To find the probability, we must calculate the area of the whole graph. Since the graph is a square with sides of $60,$ the total area of the graph is 3600 .)
Area of triangle $=\frac{45 \times 45}{2}=1012.5$
Area of both triangles $=1012.5 \times 2=2025$
(Since finding the area of a triangle is simpler than finding the area of a trapezoid, we can find the area where you don't meet your friend and subtract it from the total area which is 3600. There are two right triangles, each with sides of $45 .$ The area of
each triangle is 1012.5 units squared, and since there are
2 triangles, we double this to get 2025 )
3600 - 2025 = 1575
(Since the total area is 3600 and the area where you don't
meet is $2025,$ we subtract to get an area of 1575 for the
2 trapezoids where you do meet. )
$\frac{1575}{3600}=\frac{7}{16}$
(To find the probability that you meet your friend, we take
the area of the trapezoids where you meet and divide by
the total area of the graph. Then, simplify the fraction to
get the result. )
