Question

Monika has a piece of land which is in the shape of a rhombus.She wants her four children to work on the land and produce different crops suffice needs of their family. She divided the land in fourparts by joining its opposite corners. If the perimeter is 500m and one of the diagonals is 200 m ,how much area child will get to work out?

Answer 1

Answer:

Each child get 3750 m² area to work out.

Step-by-step explanation:

Perimeter of the Rhombus shaped field = 500 m

Length of a diagonal = 200 m

To find: Area of the triangle formed by joining the opposite corner of the rhombus( diagonals )

We know that diagonals of the rhombus bisect each other and All sides of rhombus are equal in length.

let, ABCD is Rhombus shaped field.

AC and BD are diagonals intersecting at O.

let, AC = 200 m ⇒ AO = 100 m

Perimeter = 500 m

4 × AB = 500

AB = 125 m

Now, using Pythagoras theorem in ΔAOB,

we get

AB² = AO² + BO²

125² = 100² + BO²

BO² = 15625 - 10000

BO = √5625

BO = 75 m

So, Area of ΔAOB  = 1/2 × AO × BO = 1/2 × 100 × 75 = 50 × 75 = 3750 m²

Area of all triangles = 3750 m²

Therefore, Each child get 3750 m² area to work out.