Home
Class 9
MATHS
A B C D is a parallelogram X and Y are t...

`A B C D` is a parallelogram `X` and `Y` are the mid-points of `B C` and `C D` respectively. Prove that `a r( A X Y)=3/8a r(^(gm)A B C D)` GIVEN : A parallelogram `A B C D` in which `X` and `Y` are the mid-points of `B C` and `C D` respectively. TO PROVE : `a r( A X Y)=3/8a r(^(gm)a b c d)` CONSTRUCTION : Join `B Ddot`

Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|247 Videos

  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

In Figure, A B C D is a parallelogram and X ,Y are the mid-points of sides A B and D C respectively. Show that A X C Y is a parallelogram.

In Figure, A B C D is a parallelogram and X ,Y are the mid=points of sides A B and D C respectively. Show that A X C Y is a parallelogram. Figure

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( /_\A D F)=a r( /_\D C E).

A B C D is a parallelogram and line segments A X ,\ C Y bisect the angles A\ a n d\ C , respectively. Show that A X||C Y

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. GIVEN : A parallelogram A B C D,E and F are the mid-points of opposite sides A B and C D respectively. TO PROVE : a r(||^(gm)A E F D)=a r(||^(gm)E B C F) CONSTRCUTION : Join E Fdot

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

Let A B C D be a parallelogram of area 124c m^2dot If E and F are the mid-points of sides A B and C D respectively, then find the area of parallelogram A E F Ddot

A B C D is a parallelogram. P is the mid-point of A BdotB D\ a n d\ C P intersect at Q such that C Q : Q P=3: 1. If a r\ ( P B Q)=10\ c m^2, find the area of parallelogram A B C D

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

    Text Solution

    |

  2. A B C is a triangle in which D is the mid-point of BC and E is the mid...

    Text Solution

    |

  3. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

    Text Solution

    |

  4. The diagonals of a parallelogram A B C D intersect at a point O. T...

    Text Solution

    |

  5. The medians B E\ a n d\ C F of a triangle A B C intersect at G. ...

    Text Solution

    |

  6. In Figure, compute the area of quadrilateral A B C D.

    Text Solution

    |

  7. In Figure, P Q R S is a square and T\ a n d\ U are, respectively, ...

    Text Solution

    |

  8. Compute the area of trapezium P Q R S in the given figure.

    Text Solution

    |

  9. In Figure, /A O B=90^@,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c m. ...

    Text Solution

    |

  10. In Figure, A B C D is a trapezium in which A B=7c m ,\ A D=B C=5c m ...

    Text Solution

    |

  11. In Figure, O C D E is a rectangle inscribed in a quadrant of a circl...

    Text Solution

    |

  12. In figure, A B C D is a trapezium in which A B||C D . Prove that: ...

    Text Solution

    |

  13. In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prov...

    Text Solution

    |

  14. Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect eac...

    Text Solution

    |

  15. In Figure, A B C\ a n d\ ABD are two triangles on the base A B. If ...

    Text Solution

    |

  16. If P is any point in the interior of a parallelogram A B C D , then ...

    Text Solution

    |

  17. If A D is a median of a triangle A B C ,\ then prove that triangl...

    Text Solution

    |

  18. A point D is taken on the side B C of a \ A B C such that B D=2D Cd...

    Text Solution

    |

  19. A B C D is a parallelogram whose diagonals intersect at O. If P is a...

    Text Solution

    |

  20. A B C D is a parallelogram in which B C is produced to E such that...

    Text Solution

    |