2. In a qudrilateral field sides are 8.5 m, 8.5 m, 16.5 and 14.3 m respectively and one diagonal is
15.4 m. Find the cost of turfing it at the rate of 1.50 per m².
Answers
Answer:
The total cost of turfing will be Rs 181.0.35
Step-by-step explanation:
Let's consider
a = 8.5 m
b = 8.5 m
c = 16.5 m
d = 14.3 m
and e = 15.4 m
Since we have given the measurements of four sides and one diagonal of the quadrilateral, so its divide it into two triangles.
One triangle having side a = 8.5 m b = 8.5 m and e = 15.4 m and another triangle having side c = 16.5 m d = 14.3 m and e = 15.4 m
So, the semi-perimeter of first triangle is
s\ =\ \dfrac{a+b+e}{2}s = 2a+b+e
=\dfrac{32.4}{2}=232.4
= 16.2
So, the area of triangle can be given by using heron's formula
A_1\ =\ \sqrt{s(s-a)(s-b)(s-e)}A1 = s(s−a)(s−b)(s−e)
=\ \sqrt{16.2(16.2-8.5)(16.2-8.5)(16.2-15.4)}= 16.2(16.2−8.5)(16.2−8.5)(16.2−15.4)
=\ \sqrt{16.2(7.7)(7.7)(0.8)}= 16.2(7.7)(7.7)(0.8)
=\ 27.72\ m^2= 27.72 m2
Semi-perimeter of second triangle
s\ =\ \dfrac{16.5+14.3+15.4}{2}s = 216.5+14.3+15.4
= 23.1
So, the area of triangle can be given by using heron's formula
A_2\ =\ \sqrt{s(s-c)(s-d)(s-e)}A2 = s(s−c)(s−d)(s−e)
=\ \sqrt{23.1(23.1-16.5)(23.1-14.3)(23.1-15.4)}= 23.1(23.1−16.5)(23.1−14.3)(23.1−15.4)
=\ \sqrt{23.1(6.6)(8.8)(7.7)}= 23.1(6.6)(8.8)(7.7)
=\ 97.59\ m^2= 97.59 m2
\textrm{So, total area of quadrilateral }=\ A_1\ +\ A_2So, total area of quadrilateral = A1 + A2
=\ 120.69\ m^2= 120.69 m2
Since, price of turfing is Rs 1.50 per meter square
So, the total cost of turfing will be Rs. 1.5 x 120.69 =Rs 181.0.35
Answer:
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