A farmer’s land is two adjoining trapezoids: T1 with bases 70m & 50m, height 20m; T2 with bases 50m & 30m, height 15 m. Land costs ₹60/ $m^2$. What is the total land cost?
A farmer’s land is two adjoining trapezoids: T1 with bases 70m & 50m, height 20m; T2 with bases 50m & 30m, height 15 m. Land costs ₹60/ $m^2$. What is the total land cost?
एक किसान की भूमि दो आसान्न समलंब चतुर्भुजों से बनी है: T1 जिसकी समानांतर भुजाएँ 70 मीटर और 50 मीटर हैं तथा ऊँचाई 20 मीटर है; T2जिसकी समानांतर भुजाएँ 50 मीटर और 30 मीटर हैं तथा ऊँचाई 15 मीटर है। भूमि की कीमत ₹60 प्रति $m^2$ है। कुल भूमि की कीमत क्या होगी?
Detailed Solution & Logic
₹1,08,000
Given:
T₁: Bases = 70 m, 50 m; Height = 20 m
T₂: Bases = 50 m, 30 m; Height = 15 m
Cost = ₹60 per m²
Area of T₁
$= \frac{1}{2} (70 + 50) \times 20$
$= \frac{1}{2} \times 120 \times 20$
$= 60 \times 20$
$= 1200 , m^2$
Area of T₂
$= \frac{1}{2} (50 + 30) \times 15$
$= \frac{1}{2} \times 80 \times 15$
$= 40 \times 15$
$= 600 , m^2$
Total Area
$= 1200 + 600 = 1800 , m^2$
Total Cost
$= 1800 \times 60 = 108000$
Final Answer: ₹1,08,000 / 108000 रुपये ✅
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