Answer
$\dfrac{1}{6y}$ square inches
Work Step by Step
RECALL:
The area of a triangle is given by the formula $A=\dfrac{1}{2}\text{(base)(height)}$.
Use the formula above to have:
$\\A=\dfrac{1}{2} \cdot \dfrac{5y}{6x} \cdot \dfrac{4x}{10y^2}$
Cancel the common factors to have:
$\require{cancel}
\\A=\dfrac{1}{2} \cdot \dfrac{\cancel{5y}}{\cancel{6x}3} \cdot \dfrac{\cancel{4x}2}{\cancel{10y^2}2y}
\\A=\dfrac{1}{2} \cdot \dfrac{2}{3(2y)}
\\A=\dfrac{1}{2} \cdot \dfrac{\cancel{(2)}}{3\cancel{(2y)}y}
\\A=\dfrac{1}{6y}$
