UPSC CDS Math Area and Perimeter Questions

Let AD = BC = x m and AB = CD =(x+13)m.
Perimeter of the parallelogram= 86 m
⇒x+(x+13)+x+(x+13)=86
So, AD = BC = 15 m and AB = CD = 28 m
In ΔBCD,s=

15+28+41

2

=

84

2

=42m
Using Heron’s formula,
Area of ΔBCD
=√42×27×14=14×3×3
=126m2
Remember: Diagonal of a parallelogram divides it into two triangles having equal areas.
∴Area of the parallelogram ABCD = 2 × Area of ΔBCD = 2 × 126
=252m2