Grace is budgeting for new flooring in an L-shaped living room before hosting a family gathering. The room is a 6 m by 4 m rectangle with a 2 m by 1.5 m cor...
Question 1 Report
Grace is budgeting for new flooring in an L-shaped living room before hosting a family gathering. The room is a 6 m by 4 m rectangle with a 2 m by 1.5 m corner missing, as shown in the diagram below.
- Work out the floor area of the room. (3)
Answer Details
This question finds the area of an L-shaped room by treating it as a full rectangle with a smaller rectangular corner removed.
The area of the full rectangle, ignoring the missing corner: \[ \text{Rectangle area} = 6 \times 4 = 24 \text{ m}^2 \] [1 mark]
The area of the missing corner: \[ \text{Missing corner} = 2 \times 1.5 = 3 \text{ m}^2 \] [1 mark]
Subtracting the missing corner from the full rectangle gives the actual floor area: \[ \text{Floor area} = 24 - 3 = 21.0 \text{ m}^2 \] [1 mark]
An L-shape is almost always easier to handle as "a larger simple shape minus a smaller simple shape" than by splitting it directly into an L of two separate rectangles; both methods give the same answer, but this one uses fewer measurements.
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