Kiran has a place of land which is in the shape of rhombus she decided to donate Thailand equal to an orphanage and an old age home is the perimeter of the land is 400 metre and one of the diagonal is 16 cm how much area will each get what are the values exhibited by Kiran through this donation
Answers
Required figure is as follows:
Perimeter of rhombus ABCD field = 400 m
4× side = 400 m
side = 400 m/ 4
side = 100 m
It is obvious from the figure that a diagonal BD divides the rhombus field into two triangles ABD and BCD.
We know that the diagonal of a rhombus divides it into two equal parts.
Therefore, area of ∆ ABD = area of ∆ BCD
Now, in ∆ ABD
Let a = b = 100 m and c = 16 m
Thus, semi perimeter, s = ( a + b + c ) ÷ 2
= ( 100 + 100 + 16 ) ÷ 2
= 216 ÷ 2
= 108 m
Now, by using Heron's formula
area of ∆ ABD =
= √ 108 ( 108 - 100 )( 108 - 100 ) ( 108 - 16 )
= √ 108 × 8 × 8 × 92
= √ 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 23
= 2 × 2 × 2 × 2 × 3 √ 69
= 48 √ 69
= 398. 72 m² ( approximately )
This is also the area of ∆ BCD.
Hence, each will get an area of approximately 398.72 m².
The values imbibed by Kiran through this donation are that she is selfless and is helping the needy people and helping nature.
