Week 27 · Time, floor plans and fluency · 3 lessons
2
Area of a floor plan
Discover Mathematics P3: Term 2, Lessons 101–110
GoalFind the area of rooms and floor plans in square units, including plans made of two rectangles.
New words
floor plan · a drawing of a room or house seen from abovesquare unit · a square with sides of 1 unit, used to measure areaarea · the number of square units that cover a surface
Explanation
A floor plan shows a room from above. To find the area of a rectangular room, multiply its length by its width. A room 5 units long and 4 units wide has area 5 × 4 = 20 square units, because 4 rows of 5 squares cover the floor. Some plans are made of two rectangles joined together. Find the area of each part and add: a bedroom of 4 × 3 = 12 square units and a kitchen of 3 × 3 = 9 square units have a total area of 12 + 9 = 21 square units. An L-shaped room can be cut into two rectangles in the same way. If we know the area and one side, we divide to find the other side. Always write the answer in square units.
Worked examples
The living room is 6 units long and 4 units wide. Its area is 6 × 4 = 24 square units.
Two rooms are side by side. The bedroom is 4 by 3, so its area is 12. The kitchen is 3 by 3, so its area is 9. The whole plan has area 12 + 9 = 21 square units.
This L-shaped room is cut into two rectangles. The bottom part is 6 by 2, so its area is 12. The upper part is 2 by 3, so its area is 6. The total area is 12 + 6 = 18 square units.
Class activity
Design a floor plan. On squared paper draw a flat with 3 rooms, each a rectangle, one square being one square unit. Write the length and width of each room, find each area and find the total area of the flat. Which is the biggest room?
Practice
1
A room is 7 units long and 5 units wide. What is its area?
7 × 5 = 35 square units.
2
Find the total area of the two rooms in the plan.
The left room is 5 × 3 = 15 and the right room is 2 × 3 = 6. Total: 15 + 6 = 21 square units.
3
Find the area of this L-shaped room. Cut it into two rectangles.
Cut it with a horizontal line: the bottom part is 8 × 2 = 16 and the upper part is 3 × 4 = 12. Total: 16 + 12 = 28 square units.
4
A floor is 9 units long and 6 units wide. What is the area?
9 × 6 = 54 square units.
5
A room has area 40 square units and is 8 units long. How wide is it?
