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ST-D: IX AREAS OF PARALLELOGRAMS AND TRIANGLES

(Extra Riders & Numerical sums )

1) In A ABC ,

D E and F are the midpoints of BC. AC

and AB respectively.

If ar ( A ABC) = 40 cm2

Find the ar (AEDF )

ABC,

F and D are the midpoints of the sides

AB and BC respectively

If ar (BFGD ) = 20cm2

Find the ar ( A AGC )

In II gm ABCD,

E and F are the midpoints of the sides

BC and DC respectively.

If ar ( A ABE) = 10 cm2

Find the ar ( ABCD )

ABCD is a II gm

DP = PC & BC = CQ

If ar ( A COP )= 10cm2

Find the ar (1Igm ABCD )

2)

4)

ar \ DEC) = 20cm'

Find ar ( A DFA ) If ABCD is a lIgm

In the figure, AC 11 DE

If ar) quad. ABCD) = 45 cm'

Find the area of ( A ABE )

7) In the figure.

BD = DE = EC.

If • ar 1 ABD ) = 25cm1

Find (i) ar r 1 ABE )

a ( \ ABC).

8) ABCD & BPQR are II'

ff ar ( ABCD ) = 40 cm`

Find ar ( BPQR )

ABCD is a lIgm

DC = CE

If ar ( \ ADE )= 50 cm2

Find ar (IIGm ABCD )

11) In ,AABC. D is the midpoint of AB

And CO 11 DP

Prove that art \ BOP 2 ar ( ABC )

12)

D Diagonals AC and BD of a quad ABCD

intersects at 0, such that OC = OA.

If AB = CD, prove that ABCD is a parallelogram

13) \ ABC and \ ABD are in the same base AB

CD is bisected by AB at O..

Prove that am \ ABC) = ar \ ABD )

14) In ABC, D,E & F are the midpoints of the sides AB, BC & CA respectively.

Show that ar ( DEF) = ar ( ABC).

9) ABCD is a trapezium.

Ar \ AOC) 18

10)

Find ar ( BOC

A

15) ABCD, DCFE, and ABFE are

Show that ar ( AED= ar ( BFC ) C

11) The diagonals AC and BD of a H' ABCD

Intersect at 0

Show that ar ( trap AXYD) = ar ( trap XBCY ) 4c

In the figure ar i \ BDC ) = ar (_5 BEC )

Prove that DE 11 BC.

19) In the figure ,MO = ON

Prove that ar ( S LMO ) = ar ( S AON )

O

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t•J

16) 0 ABCD is a II'

0 is anv point on the diagonal AC

Show that ar ( AOB ) = ar ( o AOD )

17) In the figure ABCD is a quad and BE II AC &

also BE meets DC produced at E.

Show that ar ADE ) = ar ( quad ABCD )

211 S and T. are the midpoints of PG and PR

If ar PQR ) = 48 cm 2

Find TSO )

22) "AZ

AD and BE are the perpendicuiars to the

Sides BC and AC of A ABC.

BC = 16cm, AC = 9.6cm & AD = 6cm ,find BE.

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