Job Roles

Area = (13.86 x 10000) sq.m = 138600 sq.m

πR2=138600⇒R2=138600×722⇒R=210m 

Circumference = 2πR2=2×227×210=1320m 

Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.

Let the two parallel sides of the trapezium be a cm and b cm. 

Then, a - b = 4 

And, 12×a+b×19=475=>a+b=50 

Solving (i) and (ii), we get: a = 27, b = 23. 

So, the two parallel sides are 27 cm and 23 cm.

Let the height of the parallelogram be x. cm. Then, base = (2x) cm.

2x×x=72=>2x2=72=>x=6 

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then, 12×x×3h12×y×4h=43⇒xy=43×43=169 

Required ratio = 16 : 9.

Let the length of the altitude be h.
Then, h = a32   = 33 × 32 = 4.5

Let ABC be the isosceles triangle and AD be the altitude 

Let AB = AC = x. Then, BC = (32 - 2x). 

Since, in an isosceles triangle, the altitude bisects the base,
so BD = DC = (16 - x).
In triangle ADC,AC2=AD2+DC2 

⇒x2=82+16-x2⇒x=10 

BC = (32- 2x) = (32 - 20) cm = 12 cm. 

Hence, required area =  12*BC*AD=12*12*8=48cm2

Area of the field = Total cost/rate = (333.18/25.6) = 13.5 hectares
13.5*10000m2=135000m2 
Let altitude = x metres  and  base = 3x metres.
Then, 12*3x*x=135000⇒x2=90000⇒x=300 

Base = 900 m and Altitude = 300 m.

Height of the triangle = 132-122=25 = 5 cm.

Its area =12*base*height= 12*12*5= 30cm2.