Question

If a fence is put parallel to the diagonal of the parallelogram field
connecting the mid points of the adjacent sides of triangle formed by the
diagonal of the parallelogram field, what will be the length of the fence?
a) 20 km b) 40 km c) 80km d) 10km

Answer 1

Step-by-step explanation:

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Join the mid points of AB, BC, CD, DA of a rhombus ABCD and name them M, N, O and P respectively to form a figure MNOP.

Joint the line PN, then PN∥AB and PN∥DC

We know that if a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to one-half area of the parallelogram.

From the above result parallelogram, ABNP and triangle MNOP are on the same base PN and in between same parallel lines PN and AB.

∴areaΔMNP=

2

1

areaABPN.................(1)

areaΔPON=

2

1

areaPNCD........................................(2)

Then area of ABCD=

2

1

×d

2

×d

2

From (i) and (ii) we get

area(MNOP)=area(ΔMNP)+area(ΔPON)

=

2

1

areaABPN+

2

1

areaPNDC

=

2

1

(

2

1

areaABCD)

=

2

1

(

2

1

×12×16)=48cm have a nice day byee