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Syllabus

1) ABCD is a paralellogram. X and Y are mid points of BC and CD respectively.Prove that area (AXY) = 3/8 area(paralellogram ABCD)

2) In a triangle ABC P and Q are respectively the mid points of AB and BC and R is the mid point of AP. Prove that:

1) area(PRQ) =1/2 area(ARC)

2) area(RQC) = 3/8 area(ABC)

3) area(PBQ) = area(ARC)

ABCD is a trapezium in which AB is parallel to DC. DC=30 cm. and AB=50cm. if X and Y are respectively the mid points of AD and BC, prove that (

Nine times the area of DCYX= seven times the area of XYBA.)

if the medians of a triangle ABC intersect at G show that ar ( AGB ) = ar(AGC)=ar(BGC)=1/3 ar(ABC).

Q.E.Din R.D.Sharma(book)?He use it after proving every theorem.

prove that two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

Q24. In the given figure, ABCD is a parallelogram. AB is produced to a point P and DP intersects BC at Q. Prove that area ($\u2206$APD) = area (quad. BPCD)

[Hint : Diagonal divides a || gm into two triangles of equal area

$\therefore $ area $\u2206$ABD = area $\u2206$DBC

Again, area $\u2206$BPD = area $\u2206$BPC ($\because $ Triangles on the same base and between the same parallel are equal in area )

prove that median divides triangle into two equal parts

The median BE and CF of a triangle ABC intersect at G. prove that area of triangle-GBC = area of quadrilateral AFGE.

E is the midpoint of diagonal BD of Parallelogram ABCD.If the point E is joined to a point F on DA such that DF= 1/3 of DA ,then ratio of th area of triangle DFE to area of quadrilateral ABEF is

a) 1 : 3 b) 1 : 4 c) 1 : 5 d)2 : 5

Diagonals AC and BD of trapezium ABCD with AB||DC intersect each other at O.

prove that ar(AOD) = ar (BOC)?

prove that the diagonals of a parallelogram divides into four triangle of an equal area

(b) ABCD is a parallelogram. BP and DQ are the perpendiculars from B and D on the diagonal AC.

(i) Show that BP = DQ.

(ii) Show that

ar ($\u25b3$ADX) = ar ($\u25b3$ABX), where X is any point in AC.ABCD is a parallelogram in which BC is produced to E such that CE = BC(Fig. 9.17). AE intersects CD at F.If ar (DFB) = 3 cm2, find the area of the parallelogram ABCD.

the sides PQ and RQ of a parallelogram PQRS are produced to L and M such that PQ =QL and RQ= QM to form another paralleogram QLNM prove that area of pallgm.PQRS=area of parllgm QLNM

in a triangle ABC,E is the midpoint of median AD. Show that area of BED = 1/4 area of ABC

6. Find the surface area of a sphere having diameter 30 cm.

The diagonals of a parallelogram ABCD intersect at point O. Through O, a line is drawn to intersect

AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal areas.

1-krishnasarp 2-parmanand 3-janmanth 4-bekhatke 5-bailghari

P and Q are respectively the mid points of side AB and BC of a triangle ABC and R is the mid point of AP show that,

{1} ar(PQR)= 1/2 ar(ARC)

{2} ar (RQC)=3/8 ar(ABC)

3) ar (pBQ) = ar(ARC)

A right triangle PQR with sides 3cm, 4cm, and 5cm is revolved about the side length 4cm. Find the volume of the shape so generated.

Prove that area of a rhombus is half the product of its diagonals.

ABCD is a rectangle and EFGH is a trapezium in the given figure. Prove that ar(ABCD) = ar(EFGH)

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that

[Hint: From A and C, draw perpendiculars to BD]

AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB=CD. Please reply ASAP. I have an exam.

D is mid point of side BC of a triangle ABC and E is mid point of BD.If O is mid point of AE , then prove that ar(BOE)=1/8ar(ABC)

How can we prove this as theorem:

Parallelogram with same base and having equal areas lie between the same parallel.

Please let me know the answer as fast as possible

If E, F, G, H ar respectively the mid points of the sides of a parallelogram ABCD, show that ar(EFGH)= 1/2 ar(ABCD)

1. EXISTENCE POSTULATE

Corresponding to each polygon P lying in a plane, there exists a real number ar(P) $\ge $ 0, called its area.

2. DOMINANCE POSTULATE

For regions ${R}_{1}and{R}_{2}$ in a plane, if ${R}_{1}\subseteq {R}_{2}$, i.e., if ${R}_{1}$ is a part of ${R}_{2}$ then ar(${R}_{1}$) $\le $ ar(${R}_{2}$).

prove that a cyclic trapezium is always isosceles trapezium.

Prove that the line segment joining the mid-points of opposites sides of a quadrilateral bisect each other.

Please help me with these sums

which PQ = PR = 20 cm and QR = 26 cm. If a

point O is marked on PS in such a way that

angle QOR = 90°, then the area of the quadrilateral

PQOR is approximately equal to

In a parallelogram PQRS, L and M are the mid-points of QR and RS respectively. Prove that :

ar(ΔPLM) = 3/8 ar( IIgm PQRS).

Please help. :)

Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show the perimeter of parallelogram is greater than rectangle.

ABC and BDE are two equilateral triangles such that D is the midpoint of BC .AE intersects BC in F.prove that::

If O is the circumcentre of Triangle ABC and OD prependicular to BC. Prove that

Angle BOD = Angle Awhat is the answer of the following question:-

in a parallelogram ABCD, P,Q,R,S are mid- points of the sides AB, CD, DA, and BC respectively. AS, BQ, CR, and DP are joined.Find the ratio of the area of the shaded region to the area of parellogram ABCD.

figure is given Below in picture

prove that in a triangle the line segment joining the mid points of any to sides is parallel to the third side.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way thatar ( AOD ) = ar ( BOC ). Prove that ABCD is a trapezium....!!I GuARAnTEeEE ThUMBS uP* FoR De CrrCt aNsaZz... ;)Q10. In $\u2206$PQR, point T is the mid-point of its median PS as shown in the figure, show that ar ($\u2206$PQT) = $\frac{1}{4}$ar ($\u2206$PQR )

(1) D and E are points on sides AB and AC respectively of triangle ABC such that ar (DBC) = ar (EBC). Prove that DE//BC

(2) Diagnols AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium

(3) Diagnols AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) x ar (CPD) = ar (APD) x ar (BPC)

CAN SOMEONE PLZZZZ GIVE THE ANSWERS TO THESE QUESTIONS .vryy imp...

Diagonals of a parallelogram are 8m and 6m respectively. If one side is 5m, then the area of Parallelogram is

a)18m

^{2}b)30m^{2}c)24m^{2}d)48m^{2}ABCD is a parallelogram.P and Q on BC trisects it.Prove that ar(APQ) =ar(DPQ)=1/6ar(ABCD)

pls no links only answers

If each diagonal of a quadrilateral seperates it into two triangles of equal area, prove that the quadrilateral is a parallelogram.

ABCD is a parallelogram, AB = 14cm, BC = 18cm, and AC = 16cm. Find the length of the other diagonal.

P and Q are any two points lying on the side DC and AD respectively of a parallelogram ABCD.Show that ar(APB)=ar(BQC).....

The line parallel to the parallel sides of a trapezium passing through the mid-points of the slant sides divide the trapezium into ratio 5:2. Then find the ratio of parallel sides

p is a point in the interior of a parallelogram

abcdshow thatarea apb +area pcd = 1/2 area abcd

area apd +area pbc =area apb+area pcd

If the mid points of the sides of a quadrilateral are joined in order, prove that the are of the parallelogram so formed will be half of the area of the given quadrilateral. Please experts answer it as quickly as possible.

In triangle PQR, PS and RT are medians and SM is parallel to RT. Prove that QM= 1/4 PQ.

XY is a line parallel to side BC of a triangle ABC. If BEAC and CFAB meet at E and F repectively. Show that ar(ABE) = ar(ACF)

^{2}. The diagonals AC and BD intersect at O. P is the mid - point of OA. Calculate area $(\u25b3BOP).$D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that

(i) BDEF is a parallelogram.

(ii) ar (DEF) = ar (ABC)

(iii) ar (BDEF) = ar (ABC)

Answer :Triangle ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that area of triangle ABC = area of triangle DBC. Show that BC bisects AD

In quadrilateral ABCD, one pair of opposite sides is equal (AB = CD) and the other pair of opposite sides is parallel (DA || CB).

Therefore, ABCD is a parallelogram.

IN NCRT Solutions of EX:9.3 sum no:6 it is given AB=CD and AD || CB therefore it ABCD is a parallelogram?

How Can this be? It can also be a trapezium and a parallelogram is a trapezium but a trapezium is not a parallelogram. An isosceles trapezium has one side parallel and in it the non-parallel sides are equal.SO I think we must say angle DCO=angle BAO (by CPCT) therfore AB parallel to Cd and AD equal to CD.Therefore Abcd is a parallelogram as 1 pair of oppt sides are equal and parallel.O is any point on the diagonal PR of a parallelogram PQRS . prove that ar(PSO) = ar(PQO) .

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT

1) ar(ADEG) = ar(GBCE), 2) ar(EGB) = 1/6 ar(ABCD) , 3) ar(EFC) = 1/2 ar(EBF) , 4) ar(EBG) = ar(EFC) , 5) FIND WHAT PORTION OF THE ARE OF PARALLELOGRAM IS THE AREA OF EFG.

ABCD is a quadrilateral. A line through D,parallel to AC meets BC produced in P. Prove that area of triangle APD= area of quadrilateral ABCD.

The semiperimeter of a triangle is 96 cm and its sides are in the ratio of 3:4:5. Find the area of the triangle.,

a farmer has a square plot of land where he wants to grow five different crops at a time . on half of the area in the middle he wants to grow wheat but in rest four equal triangular parts he wants to grow different crops.

a. explain by diagram how he can divide the area to fulfill his purpose .

b. by using this crop pattern which values are depicted by the farmer

A triangle ABCis right angled at A. AL is drawn perpendicular to BC. Prove thatangle BAL =angle ACBABCDE is a pentagon.A line passing through B parallel to AC meets DC produced at F.Show that

ar(ACB)=ar(ACF)

ar(AEDF)=ar(ABCDE)

explain with figure

prove that parallelogram on the same base and between the same parallel are equal in area

WHAT IS AREA AXIOMS,CONGRUENT AREA AXIOMS,AREA MONOTONE AXIOM,AREA ADDITION AXIOM AND RECTANGLE AREA AXIOM

The circumcentre of the triangle ABC is O. Prove that angle OBC+angle BAC=90 degree. Please answer fast!!!!!!

If a triangle is divided into four pieces with areas 8 , 5 , 10 and x then find x.

ABC and ABD are two Triangles on lthe same base AB. If line segment CD is bisected by AB at O, Show that ar(ABC) = ( ABD)

if perimeter of a right angled triangle is six times its smallest side,then the three sides of this triangle are in the ratio of

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F.

Prove that ar( ADF ) = ar (ABFC ).

In triangle ABC, AD is the median and DE || AB. Prove that BE is another median.

Please help! :O

Sorry, i couldn't post the figure.

Draw the frequency polygon representing the following frequency distribution: -

Diff. b/w the outer lateral surface area and inner lateral sur. area of cylindrical metallic pipe 28 cm long is 176 sq. cm.Find the outer and inner radii of the pipe, if the pipe is made 352 cubic cm of metal.

Construct an isosceles triangle whose perimeter is 12 cm and altitude is 4 cm.

If the non parallel sides of trapezium are equal prove that it is cyclic.

ABCD is a trapezium with AB parallel to DC. a line parallel to AC intersects AB to X and BC to Y. prove that ar(ADX)=ar(ACY).

What is the difference between a quadrilateral and parralellogram.??

The diagonals of quad. ABCD intersect at O .Prove that if BO = OD, then ar (triangle ABC) = ar (triangle ADC).

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that area of the triangle is equal to half the area of the parallelogram.

rnMy teacher is saying that it is a theoram plz tell me by proving it...

a transversal cuts two parallel lines . prove that the bisectors of the interior angles endose a rectangle

ar(BPQ)=1/2ar(ABC

ABCD is a parallelogram having area of 450cm square.If ABllCD,P and Q divide AB and CD in the ratio 1:2, find the area of the parallelogram APQD and parallelogram PBCQ.

the base of a triangular field is three times its altitude.if the cost of sowing the field at rs 58 per hectare is rs 783,find its base and height.

ABCD is a trapezium with AB parallel to CD.LM is the line joining midpoints of AD and BC respectively.It is given that LM parallel to AB.Prove that

LM=1/2(AB+DCABCD is a parallelogram and BC is produced to point Q such that AD=CQ. If AQ intersects DC at P, show that ar(triangle BPC)=ar(triangle DPQ)

Triangle ABCand triangle ABD are two triangle on the same base AB.If line segment CD is bisected by AB at O, show that area [triangleABC]=area [triangleABD].