Advertisements
Advertisements
प्रश्न
In the following figure, DE is parallel to BC.
Show that:
(i) Area ( ΔADC ) = Area( ΔAEB ).
(ii) Area ( ΔBOD ) = Area( ΔCOE ).
Advertisements
उत्तर
(i) In ΔABC, D is the midpoint of AB and E is the midpoint of AC.
`"AD"/"AB" = "AE"/"AC"`
DE is parallel to BC.
∴ A( ΔADC ) = A( ΔBDC ) = `1/2` A( ΔABC )
Again,
∴ A( ΔAEB ) = A( ΔBEC ) = `1/2` A( ΔABC )
From the above two equations, we have
Area( ΔADC ) = Area( ΔAEB ).
Hence Proved.
(ii) We know that the area of triangles on the same base and between the same parallel lines are equal.
Area( ΔDBC )= Area( ΔBCE )
Area( ΔDOB ) + Area( ΔBOC ) = Area( ΔBOC ) + Area( ΔCOE )
So, Area( ΔDOB ) = Area( ΔCOE ).
APPEARS IN
संबंधित प्रश्न
The given figure shows the parallelograms ABCD and APQR.
Show that these parallelograms are equal in the area.
[ Join B and R ]
In the given figure, ABCD is a parallelogram; BC is produced to point X.
Prove that: area ( Δ ABX ) = area (`square`ACXD )
ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N.
Prove that: area of Δ ADM = area of Δ ACN.
In the given figure, diagonals PR and QS of the parallelogram PQRS intersect at point O and LM is parallel to PS. Show that:
(i) 2 Area (POS) = Area (// gm PMLS)
(ii) Area (POS) + Area (QOR) = Area (// gm PQRS)
(iii) Area (POS) + Area (QOR) = Area (POQ) + Area (SOR).
In parallelogram ABCD, P is a point on side AB and Q is a point on side BC.
Prove that:
(i) ΔCPD and ΔAQD are equal in the area.
(ii) Area (ΔAQD) = Area (ΔAPD) + Area (ΔCPB)
The given figure shows a pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and CF draw parallel to DB meets AB produced at F.
Prove that the area of pentagon ABCDE is equal to the area of triangle GDF.
ABCD is a parallelogram in which BC is produced to E such that CE = BC and AE intersects CD at F.
If ar.(∆DFB) = 30 cm2; find the area of parallelogram.
The given figure shows a parallelogram ABCD with area 324 sq. cm. P is a point in AB such that AP: PB = 1:2
Find The area of Δ APD.
In ΔABC, E and F are mid-points of sides AB and AC respectively. If BF and CE intersect each other at point O,
prove that the ΔOBC and quadrilateral AEOF are equal in area.
Show that:
The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.
