Multiple choice

Lisa plans to decorate the ceiling of her small cuboidal-shaped room. She knows that the total surface area of the room is 56 square meters, with a lateral surface area of 36 square meters. What is the area, in square meters, of the ceiling that she plans to decorate?

  1. 7

  2. 8

  3. 9

  4. 10

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total surface area = 2(lb + bh + lh) = 56. Lateral surface area = 2h(l+b) = 36. Total surface area = Lateral + 2(lb) = 56. 36 + 2(lb) = 56, so 2(lb) = 20, lb = 10. The area of the ceiling is lb = 10.

AI explanation

The total surface area of a cuboid is the sum of its lateral surface area and the area of its base and top. Since the area of the ceiling is the area of one base, we can calculate it by subtracting the lateral surface area from the total surface area and dividing by two. This gives (56 minus 36) divided by 2, which equals 20 divided by 2, resulting in an area of 10 square meters.

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