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) ?COP and ?AQD are equal in the area.
(ii) Area (?AQD) = Area (?APD) + Area (?CPB)
In the following figure, CE is drawn parallel to diagonal DB of the quadrilateral ABCD which meets AB produced at point E.
Prove that triangle ADE and Quadrilateral ABCD are equal in area.
In the given figure, AP is parallel to BC, BP is parallel to CQ. Prove that the areas of triangles ABC and BQP are equal.
In the following figure, DE is parallel to BC. Show that:
(i) Area (∆ADC) = Area (∆AEB)
(ii) Area (∆BOD) = Area (∆COE)
. ABCD and BCFE are parallelograms. If area of triangle EBC=480cm2 , AB=30cm and BC=40cm; Calculate;
(i) Area of parallelogram ABCD;
(ii) Area of parallelogram BCFE;
(iii) Length of altitude from A on CD;
(iv) Area of triangle ECF.
In the given figure, D is the mid-point of side AB of ∆ABC and BDEC is a parallelogram. Prove that:
Area of ∆ABC = Area of ||gm BDEC.
In the following figure, AC||PS||QR and PQ||DB||SR. Prove that:
Area of Quadrilateral PQRS = 2 x Area of quad. ABCD.
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 triangle ADM = area of triangle ACN
In the given figure,
AD||BE||CF.
Prove that:
Area (∆AEC) = Area (∆DBF)
The given figure shows the parallelograms ABCD and APQR. Show that these parallelograms are equal in the area.
[Join B and R]
Show that:
(i) A diagonal divides a parallelogram into two triangles of equal area.
(ii) The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.
(iii) The ratio of the areas of two triangles of the same base is equal to the ratio of their heights.
In the given figure; AD is the median of ∆ABC and E is any point on median AD. Prove that area of triangle ABE = area of triangle ACE.
ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD respectively. Prove that area of triangle APQ= 1/8 of the parallelogram ABCD.
The base BC of triangle ABC is divided at D so that BD=1/2 DC. Prove that area of the triangle ABD=1/3 of the area of triangle ABC.
In a parallelogram ABCD, point P lies in DC such that DP: PC=3:2. If the area of triangle DPB=30 sq. cm, find the area of the parallelogram ABCD.
The following figure shows a triangle ABC in which P, Q, and R are mid-points of sides AB, BC and CA respectively. S is the mid-point of PQ.
Prove that: ar.(∆ ABC) = 8 x ar.(∆ QSB)
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 ∆APD.
In parallelogram ABCD, P is the mid-point of AB. CP and BD intersect each other at point O. If the area of triangle POB = 40 cm2 and OP:OC = 1:2, find:
(i) Areas of triangle BOC and PBC
(ii) Areas of triangle ABC and parallelogram ABCD.
The medians of a triangle ABC intersect each other at point G. If one of its medians is AD, prove that:
(i) Area (∆ABD) = 3 × Area (∆BGD)
(ii) Area (∆ACD) = 3 × Area (∆CGD)
(iii) Area (∆BGC) = 1/3 × Area (∆ABC)
The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6:5:4. Find the lengths of its sides.
In the following figure, OAB is a triangle and AB||DC. If the area od triangle CAD = 140 cm2 and the area of triangle ODC = 172 cm2 , find
(i) The area of triangle DBC
(ii) The area of triangle OAC
(iii) The area of triangle ODB
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