Pls Answer Q.58.
Need Qualitative Answer with excellent explanation .
Answers
Given :
PQRS is a parallelogram:
- with N as midpoint of SR.
- with M as midpoint of RQ
IMPORTANT THINGS TO NOTE
⇒ When a triangle is formed by the midpoint of one side of a parallelogram and the adjacent side's vertices then the area of triangle will be 1/4 × area of parallelogram
Eg : Δ PNS
⇒ Also when the triangle is formed by joining 2 midpoints of adjacent sides and the vertex between them , then the area of triangle will be 1/8 × area of parallelogram .
Eg : RNM
Area of Δ PNS
Area of Δ PNS = 1/4 × area of PQRS [ N is the midpoint ]
Area of Δ RNM
Area of Δ RNM = 1/8 × area of PQRS [ N and M are the midpoints ]
Area of Δ PMQ
Area of Δ PMQ = 1/4 × area of PQRS [ M is the midpoint ]
Area of Δ PMN
Area of Δ PMN = Area of parallelogram - ( Area of Δ PMQ + Area of ΔRNM + Area of ΔPNS )
= Area of PQRS - ( 1/4 × Area (PQRS) + 1/8 × Area (PQRS) + 1/4 ×Area(PQRS) )
= Area ( PQRS ) [ 1 - ( 1/4 + 1/8 + 1/4 ) ]
= Area ( PQRS ) [ 1 - ( 2 + 2 + 1 ) / 8 ]
= Area ( PQRS ) [ 1 - 5/8 ]
= Area ( PQRS ) ( 8 - 5 ) / 8
= Area ( PQRS ) 3/8
The area will be 3/8 × area of PQRS
3/8 × Area( PQRS ) = Area ( Δ PMN )
==> Area ( PQRS ) = 8/3 × Area (ΔPMN)
Hence area of PQRS = 8/3 × Area of Δ PMN
Hope it helps !
And Happy new year :-)
____________________________________________________________________
Answer:
Step-by-step explanation:
PQRS is a parallelogram:
with N as midpoint of SR.
with M as midpoint of RQ
IMPORTANT THINGS TO NOTE
⇒ When a triangle is formed by the midpoint of one side of a parallelogram and the adjacent side's vertices then the area of triangle will be 1/4 × area of parallelogram
Eg : Δ PNS
⇒ Also when the triangle is formed by joining 2 midpoints of adjacent sides and the vertex between them , then the area of triangle will be 1/8 × area of parallelogram .
Eg : RNM
Area of Δ PNS
Area of Δ PNS = 1/4 × area of PQRS [ N is the midpoint ]
Area of Δ RNM
Area of Δ RNM = 1/8 × area of PQRS [ N and M are the midpoints ]
Area of Δ PMQ
Area of Δ PMQ = 1/4 × area of PQRS [ M is the midpoint ]
Area of Δ PMN
Area of Δ PMN = Area of parallelogram - ( Area of Δ PMQ + Area of ΔRNM + Area of ΔPNS )
= Area of PQRS - ( 1/4 × Area (PQRS) + 1/8 × Area (PQRS) + 1/4 ×Area(PQRS) )
= Area ( PQRS ) [ 1 - ( 1/4 + 1/8 + 1/4 ) ]
= Area ( PQRS ) [ 1 - ( 2 + 2 + 1 ) / 8 ]
= Area ( PQRS ) [ 1 - 5/8 ]
= Area ( PQRS ) ( 8 - 5 ) / 8
= Area ( PQRS ) 3/8
The area will be 3/8 × area of PQRS
3/8 × Area( PQRS ) = Area ( Δ PMN )
==> Area ( PQRS ) = 8/3 × Area (ΔPMN)
Hence area of PQRS = 8/3 × Area of Δ PMN