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A room has dimensions L=5m, W=3m, H=2.5m. A door has dimensions 1.5m by 0.9m. Calculate the area to be painted.

Mathematics

ScanSolve AI Answer

Answer

38.65 m2\text{38.65 m}^2

Step-by-step solution

3 steps
  1. Calculate the total surface area of the four walls of the room.

    The formula for the area of the four walls of a rectangular room is 2(L×H)+2(W×H)2(L \times H) + 2(W \times H), where LL is length, WW is width, and HH is height.
    Given: L=5L = 5 m, W=3W = 3 m, H=2.5H = 2.5 m.

    Area of walls=2(5 m×2.5 m)+2(3 m×2.5 m)\text{Area of walls} = 2(5 \text{ m} \times 2.5 \text{ m}) + 2(3 \text{ m} \times 2.5 \text{ m}) Area of walls=2(12.5 m2)+2(7.5 m2)\text{Area of walls} = 2(12.5 \text{ m}^2) + 2(7.5 \text{ m}^2) Area of walls=25 m2+15 m2\text{Area of walls} = 25 \text{ m}^2 + 15 \text{ m}^2 Area of walls=40 m2\text{Area of walls} = 40 \text{ m}^2
  2. Calculate the area of the door.

    The formula for the area of a rectangle is length ×\times width.
    Given: door dimensions are 1.5 m by 0.9 m.

    Area of door=1.5 m×0.9 m\text{Area of door} = 1.5 \text{ m} \times 0.9 \text{ m} Area of door=1.35 m2\text{Area of door} = 1.35 \text{ m}^2
  3. Calculate the total surface area that will be painted.

    This is the area of the walls minus the area of the door.

    Painted area=Area of walls−Area of door\text{Painted area} = \text{Area of walls} - \text{Area of door} Painted area=40 m2−1.35 m2\text{Painted area} = 40 \text{ m}^2 - 1.35 \text{ m}^2 Painted area=38.65 m2\text{Painted area} = 38.65 \text{ m}^2

    The total surface area that will be painted is 38.65 m2\boxed{\text{38.65 m}^2}.


    For question 8, the problem statement is incomplete as it describes the object and its dimensions but does not ask a specific question (e.g., to calculate its volume, surface area, or mass).

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