a plot of land has a shape of a parallelogram it is to be covered by mud find the cost of spreading mud at the rate of rupees hundred per square metre while the adjacent side of the plot are 39 m and 25 m metre and the diagonal is 56 m.
Answers
The cost of spreading mud at the rate of rupees hundred per square metre Rs. 84000.
Step-by-step explanation:
Dimensions of the parallelogram-shaped plot:
Since opposite sides of parallelogram are equal so, we have
AB = CD = 39 m and BC = AD = 25 m
Diagonal, AC = 56 m
(as shown in the figure attached below)
We know that that the diagonal of a parallelogram bisects the parallelogram into two congruent triangles, therefore, we get
Area of parallelogram = Ar(∆ABC) + Ar(∆ADC) = 2 * Ar(∆ABC) …… (i)
Now, in ∆ABC, we have
AB = a = 39 m, BC = b = 25 m and AC = c = 56 m
S = = 60
∴ Area of ∆ABC is given by,
=
=
=
=
= 420 m² ….. (ii)
From (i) & (ii), we get
Area of parallelogram = 2 * Ar(∆ABC) = 2 * 420 = 840 m²
The cost of spreading the mud is given as Rs. 100/m²
Thus,
The total cost of spreading across the entire parallelogram-shaped plot is,
= Rs. 100 * 840 m²
= Rs. 84000
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