The total area of four walls of a room is 660 m2 and the length is twice its…

Concept: For a cuboidal room, the total area of the four walls (the lateral surface area) is given by 2h(l + w), where h is the height, l the length, and w the width. The ceiling (and the floor) of the room is a rectangle of area l × w, so once l and w are known from the wall-area equation, the ceiling area follows directly.

Application:

1. Let the width be w, so the length l = 2w, since the length is twice the width.

2. Apply the four-wall formula with h = 11 m: 2 × 11 × (l + w) = 660, i.e. 2 × 11 × (2w + w) = 660.

3. Simplify the bracket: 2 × 11 × 3w = 660, which gives 66w = 660.

4. Solve for the width: w = 660 ÷ 66 = 10 m.

5. Find the length: l = 2w = 2 × 10 = 20 m.

6. Compute the ceiling area: l × w = 20 × 10 = 200 m2.

Cross-check: Substituting l = 20 m and w = 10 m back into the wall-area formula gives 2 × 11 × (20 + 10) = 22 × 30 = 660 m2, which matches the total wall area stated in the question. So the dimensions are consistent, and the ceiling area is 200 m2.