Worked Example 1
A rectangular field is 45 m long and 28 m wide. Find the cost of fencing at Rs 120 per metre and turfing at Rs 65 per square metre.
Decide which is whichFencing goes round the edge, so perimeter. Turf covers the inside, so area.
PerimeterP = 2(45 + 28) = 146 m. Fencing = 146 × 120 = Rs 17,520.
AreaA = 45 × 28 = 1260 m². Turf = 1260 × 65 = Rs 81,900.
Sense checkTurfing costs far more than fencing, which is what you would expect.
Worked Example 2
An L-shaped room. The outer rectangle is 8 m by 6 m with a 3 m by 2 m corner missing. Find its area two ways.
Method 1: subtract48 - 6 = 42 m²
Method 2: split and add32 + 10 = 42 m², the same answer by a different route.
Why do it twiceTwo independent methods agreeing is far stronger evidence than one method done carefully.
And the perimeterWalk right round the outside: 8 + 6 + 3 + 2 + 5 + 4 = 28 m. The cutting line is inside and is not fencing.
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