UPSC CDS 1 2022 Math Paper

Given:
The perimeter of the rhombus is 100m
One of the diagonals is 40m
Formula Used:
Area of a triangle having sides a,b,c is
A=√s(s−a)(s−b)(s−c)
Where, S (semi perimeter )=(a+b+c)∕2
Concept Used:
The sides of the rhombus are equal Calculation: According to the question
Sides of rhombus =100∕4=25m
So, AB=25m,AD=25m , and BD=40m (given)
S (semi perimeter )=(25+25+40)∕2=45m
⇒ Area of =√s(s−a)(s−b)(s−c)
⇒ Area of △ABD=√‌45×20×20×5
⇒ Area of ∆ABD=300m2
So, The area of whole rhombus =300×2=600m2
∴ The area of each part is 600÷4=150m2 .