Home
Class 9
MATHS
In the figure, ABCD is a quadrilateral. ...

In the figure, ABCD is a quadrilateral. A line DP drawn parallel to diagonal AC from point D, meet BC produced at P. Prove that:
area of `Delta ABP = " area of " square ABCD`

Text Solution

Verified by Experts

Here `AC|\ |DP` (given)
`DeltaACP` and `DeltaACD` are on same base AC and between the same parallel lines AC and DP.
`therefore` area of `DeltaACP=` area of `squareABCD`
Adding area of `Delta ABC` on both sides.
area of `DeltaACP+` area of `DeltaABC=` area of `DeltaACD+` area of `DeltaABC`
`rArr` area of `DeltaABP=` area of `square ABCD`.
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/exemplar|12 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN|Exercise Exercise|34 Videos

  • CIRCLE

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Questions )|5 Videos

Similar Questions

Explore conceptually related problems

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P . Prove that ar(triangleABP)=ar("qaud. ABCD") .

ABCD is a quadrilateral. The straight line through C parallel to the diagonal DB intersects AB produced at E. Prove that the ar(quad. ABCD) = ar (triangleADE) .

O' is any point on diagonal AC of a parallelogram ABCD. Prove that : area of Delta AOD = " area of " Delta AOB

In the adjoining figure, ABCD is a quadrilateral in which AD ||BC . AC and BD intersect each other at point 'O'. Prove that: area of Delta COD = " area of " Delta ABO

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that ar( Delta AEDF) = ar( Delta ABCDE)

The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is

In Figure,ABCD is a quadrilateral and BE perp AC and at at a BE mets DC produced at E, Show that area of $ADE is equal to the area of the quadrilateral ABCD .

In the adjoining figure, the area of quadrilateral ABCD is

In Figure,ABCD is a quadrilateral and BE|AC and also BE meets DC produced at E show that area of ADE is equal to the area of the quadrilateral ABCD

In figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (DeltaAPQ) .