Question

Sanya has a piece of land which is in the shape of a rhombus
. She wants her one daughter and one son to work on the land and
produce different crops. She divided the land in two equal parts. If the perimeter of
the land is 400 m and one of the diagonals is 160 m, how much area each of them will
get for their crops?
​

Answer 1

Topic :-

Mensuration

Given :-

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. The perimeter of the land is 400 m and one of the diagonals is 160 m.

To Find :-

Area each of them will get for the crops.

Formulae to be Used :-

Perimeter of Rhombus = 4 × Side

Area of Rhombus = ( Product of diagonals ) / 2

Concept :-

Length of Diagonals in Rhombus aren't equal.

The diagonals of a rhombus bisect each other at right angles.

Solution :-

Perimeter of Rhombus = 400 m

4 × Side = 400 m

Side = 100 m

Length of one diagonal = 160 m

Now,

Apply Pythagoras from in one of triangle, (refer to the attachment)

( Side )² = ( Half of first Diagonal )² + ( Half of second Diagonal )²

( 100 )² = ( 80 )² + ( Half of second Diagonal )²

( Half of second Diagonal )² = ( 100 )² - ( 80 )²

( Half of second Diagonal )² = ( 60 )²

( Half of second Diagonal ) = 60 m

Length of second Diagonal = 2 × 60 m

Length of second Diagonal = 120 m

Now,

Area of Rhombus = ( Product of Diagonals ) / 2

Area of Rhombus = ( 160 × 120 ) / 2

Area of Rhombus = 160 × 60 m²

Area of Rhombus = 9600 m²

As we know, area is divided into two equal parts.

So, area each of them will get = 9600 m² / 2

So, area each of them will get = 4800 m²

Answer :-

So, area each of them will get is 4800 m².