Question

The plan and measurement for a house are given in the figure. The house is surrounded by a path 1 m wide.

Find the following:

1. Cost of paving the path with bricks at rate of ₹ 120 per m².
2. Cost of wooden flooring inside the house except the bathroom at the cost of ₹ 1200 per m².
3. Area of Living Room.

Answer 1

i. Area of path = Area of rectangle PQRS – Area of rectangle ADFH

= PQ × QR – AD × DF

= (4 + 2.5 + 4 + 1 + 1) × (3 + 3 + 1 + 1) – (4 + 2.5 + 4) × (3 + 3) 

= 12.5 × 8 – 10.5 × 6 

= 37 m² 

∴ Cost of paving the path with bricks = Cost per unit m² × Total area of path

= 120 × 37

= ₹ 4440

ii. Area of house except bathroom = Area of house – Area of bathroom

= Area of rectangle ADFH – Area of rectangle BCLK

= (4 + 2.5 + 4) × (3 + 3) – 2.5 × 2 

= 63 – 5

= 58 m²

∴ Cost of flouring = Cost per unit m² × Total area

= 1200 × 58

= ₹ 69600

iii. Area of living room = Area of rectangle ACGH – Area of rectangle ABJI  – Area of rectangle BCLK

= (4 + 2.5) × (3 + 3) – 4 × 3 – 2.5 × 2

= 39 – 12 – 5

= 22 m²