What is the area of the shaded region below?
I think the solution requires subtracting the area of each of the four triangles from the area of the rectangle. I can calculate the area of triangles a and b since I have a base and height. But I don't see how to calculate the height of triangles c and d.
I've tried drawing a line parallel to the 3 cm width of the rectangle that intersects with the point where triangles c and d touch. The height of that line (call it h) along the 4 cm height of the rectangle would give me the height of both triangles c and d. But I don't see how to derive h.
Best Answer
The heights of $c$ and $d$ are in the ratio $1:3$ (equal to the ratio of their bases). So the heights are $1$ and $3$ respectively.
The area is $$3\times 4-\frac{1}{2}\times 1\times 4-\frac{1}{2}\times 1\times 4-\frac{1}{2}\times 1\times 1-\frac{1}{2}\times 3\times 3$$