The probability that the counter falls inside the trapezoid can be calculated by comparing the area of the trapezoid and the total area.
The area of a trapezoid of bases b1 and b2, and height h is:
[tex]A_t=\frac{b_1+b_2}{2}\cdot h[/tex]
The longer base measures b1 = 7 and the shorter base measures b2 = 3. The height is the horizontal distance between the bases, thus h = 6.
Substituting:
[tex]\begin{gathered} A_t=\frac{7+3}{2}\cdot6 \\ A_t=30 \end{gathered}[/tex]
The total area of the grid is 10 × 10 = 100.
The required probability is:
[tex]p=\frac{30}{100}=\frac{3}{10}=0.3[/tex]
The probability is 3/10 or 0.3 or 30%
