Question

Find the perimeter of each room

Total perimeter of all the rooms
Find the area of each room
Find the total area of all the rooms

Answer 1

The expression representing the perimeter and area are;

1. Perimeter of Room 1 is; 10·x + 10
2. Perimeter of Room 2 is; 4·x + 16
3. Perimeter of Room 3 is; 8·x + 2
4. Perimeter of Room 4 is; 12·x - 16
5. The perimeter of all the rooms = 26·x + 6
6. Area of Room 1 is; 4·x² + 17·x + 4
7. Area of Room 2 is; x² + 8·x + 7
8. Area of Room 3 is; 3·x² + 3·x
9. Area of Room 4 is; 5·x² + 21·x - 54
10. The total area of all the rooms is; 13·x² + 49·x - 43

The detailed steps used to arrive at the above solution are as follows;

Perimeter of Room 1 is; 2 × (4·x + 1) + 2 × (x + 4) = 10·x + 10

Perimeter of Room 2 is; 2 × (x + 7) + 2 × (4·x + 1 - 3·x) = 4·x + 16

Perimeter of Room 3 is; 2 × (x + 1) + 2 × 3·x = 8·x + 2

Perimeter of Room 4 is; 2 × (x + 6) + 2 × (5·x - 9) = 12·x - 6

The total perimeter of all the rooms can be found using the following equation obtained from the diagram

4·x + 1 + x + 4 + x + 7 + 3·x + 3·x + x + 1 + 3·x + (5·x - 9 - (4·x + 1 - 3·x)) + x + 6 + (5·x - 9) + x + 7 - (x + 1) = 26·x + 6

The perimeter of all the rooms = 26·x + 6

Area of Room 1 is; (4·x + 1) × (x + 4) = 4·x² + 17·x + 4

Area of Room 2 is; (x + 7) × (4·x + 1 - 3·x) = x² + 8·x + 7

Area of Room 3 is; (x + 1) × 3·x = 3·x² + 3·x

Area of Room 4 is; (x + 6) × (5·x - 9) = 5·x² + 21·x - 54

The total area of all the rooms is therefore;

Area of all the rooms is; 4·x² + 17·x + 4 + x² + 8·x + 7 + 3·x² + 3·x + 5·x² + 21·x - 54 = 13·x² + 49·x - 43