Home
Class 9
MATHS
In a A B C ,E is the mid-point of med...

In a ` A B C ,E` is the mid-point of median `A Ddot` Show that `ar ( B E D)=1/4 ar ( A B C)`

Text Solution

Verified by Experts

Since `AD` is the median of `/_\ABC.`
`:. ar(/_\ABD =(/_\ ADC)`
`ar(/_\ABD)= 1/2ar(/_\ABC)......(1)`
In `/_\ ABD`,
`BE` is the median,
`ar(/_\BED)= ar(/_\BAE)`
`ar(/_\BED)=1/2 ar(ABD)`
`ar(/_\BED)=1/2 xx 1/2 ar (/_\ABC)`
From eq `(1)`
`=ar(/_\BED)=1/4 ar(/_\ABC)`
Hence proved.
Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA|Exercise All Questions|247 Videos

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC,E is the mid-point of median AD.Show that quad ar(BED)=(1)/(4)ar(ABC)

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

In a triangle ABC, E is the mid-point of median AD. Show that ar (triangleBED)=1/4 ar( triangleABC ).

D is the mid-point of side B C of \ A B C\ a n d\ E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r\ (\ B O E)=1/8a r\ (\ A B C)

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r( B D E)=1/4a r\ (\ A B C)

In A B C ,\ E is the mid-point of median A D such that B E produced meets A C\ at Fdot If A C=10. 5\ C M , then A F= 3cm (b) 3.5cm (c) 2.5cm (d) 5cm

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

Any point D is taken in the base B C of a triangle A B C\ a n d\ A D is produced to E , making D E equal to A Ddot Show that a r\ ( B C E)=a r( A B C)

In Fig.9.23,E is any point on median AD of a Delta ABC Show that ar (ABE)=ar(ACE)

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r\ (\ F E D)=1/8a r\ (\ A F C)

RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. Show that a median of a triangle divides it into two triangles of eq...

    Text Solution

    |

  2. A D is one of the medians of a A B Cdot. X is any point on AD . S...

    Text Solution

    |

  3. In a A B C ,E is the mid-point of median A Ddot Show that ar ( B E ...

    Text Solution

    |

  4. In Figure, A B C D is a quadrilateral and B E|A C and also B E meets...

    Text Solution

    |

  5. Diagonals A C and B D of a trapezium A B C D with A B||D C intersect...

    Text Solution

    |

  6. In Figure, A B C D E\ is a pentagon. A line through B parallel to A...

    Text Solution

    |

  7. Show that the diagonals of a parallelogram divide it into four trian...

    Text Solution

    |

  8. The diagonals of quadrilateral A B C D ,AC and B D intersect in O...

    Text Solution

    |

  9. If the diagonals A C ,\ B D of a quadrilateral A B C D , intersect...

    Text Solution

    |

  10. If each diagonals of a quadrilateral separates it into two triangles...

    Text Solution

    |

  11. Show that the area of a rhombus is half the product of the lengths o...

    Text Solution

    |

  12. The side AB of a parallelogram ABCD is produced to any point P. A line...

    Text Solution

    |

  13. A villager Itwari has a plot of land of the shape of a quadrilateral...

    Text Solution

    |

  14. A B C D is a trapezium with A B|\|D C . A line parallel to A C int...

    Text Solution

    |

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

    Text Solution

    |

  16. In Figure, A P B Q\ C Rdot Prove that a r\ ( A Q C)=\ a r\ (P B R)

    Text Solution

    |

  17. In Fig.9.29, a r\ (B D P)\ =\ a r\ (A R C)and a r\ (B D P)\ =\ a r\ (A...

    Text Solution

    |

  18. Diagonals A C and B D of a quadrilateral A B C D intersect at O in suc...

    Text Solution

    |

  19. In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O...

    Text Solution

    |

  20. A point O inside a rectangle A B C D is joined to the vertices. Prov...

    Text Solution

    |