Two squares with sides of lengths 2 and 4 are arranged side-by-side, as shown below, so that one side of each square lies on line AB and a segment connects the bottom left corner of the smaller square to the upper right corner of the larger square. What is the area of the shaded quadrilateral?
I cant attach the picture, but the area of the shaded quadrilateral is refering to the section of the bigger quadrilateral, the one with side lengths 4 and the lower section, that lies on line AB.
< I cant attach the picture >
The pic can be seen at https://www.gauthmath.com/solution/1725613842539525
From the image provided, we see that the line forms a triangle with an area of \(6 \times 4 \div 2 = 12\).
The smaller, unshaded triangle is similar to the large triangle, with a side ratio of \(1 \over 3\). This means that area of the small triangle is \(1 \over 9\)th of the bigger triangle.
Can you take it from here?