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Question
The plan and measurement for a house are given in the following figure. The house is surrounded by a path 1 m wide.
Find the following:
- Cost of paving the path with bricks at rate of ₹ 120 per m2.
- Cost of wooden flooring inside the house except the bathroom at the cost of ₹ 1200 per m2.
- Area of Living Room.
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Solution
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
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