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Area of shaded triangle = (1/2) * base * height = (1/2)(10 – 4)4 = 2 * 6 = 12m²

Let w be the width of the overlapped rectangle.  Its length is 4m.

Since the area of the overlapped rectangle and triangle is 18m²,

4w + 12 = 18
4w = 6
w = 3/2 m

So the width of the uncovered rectangle = 10 – (3/2) = 17/2m

The length of the uncovered rectangle = 6 + 6 = 12m

So area of uncovered rectangle = 12 * (17/2) = 102m²

The rectangle at the corner has the same area as the shaded triangle, ie. = 12m²

So total area of floor not covered by carpets = 102 + 12 = 114m² #

PS. This problem is not difficult.  Just tedious 🙂

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