Home
Class 9
MATHS
A B C D is a parallelogram. P is the ...

`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`

Text Solution

Verified by Experts

Let CQ=3x and PQ=x
ar(`trianglePBQ`)=`10cm^2`
As we know that, Area of triangle = `1/2 xx Base xx Height`
Area (`trianglePBQ`) = `1/2xxXxxh`
`Xxxh=20`
Area of `triangleBQC`=`1/2xx3Xxxh`
=`1/2xx3xx20`
=`30cm^2`
...
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

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that: C Q=1/3B Cdot Prove that A Q C P is a parallelogram.

P Q R S is a trapezium having P S\ a n d\ Q R as parallel sides. A is any point on P Q\ a n d\ B is a point on S R such that A B Q R . If area of P B Q is 17\ c m^2, find the area of \ A S R

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

P is any point on base B C of A B C\ a n d\ D is the mid-point of B CdotD E is drawn parallel to P A to meet A C at Edot If a r\ ( A B C)=12 c m^2 , then find area of E Q C

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

In Fig. 9.32, ABCD is a parallelogram and BC is produced to a point Q such that A D" "=" "C Q . If AQ intersect DC at P, show that a r" "(B P C)" "=" "a r" "(D P Q)dot

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. A B C is a triangle in which D is the mid-point of B C , E and F a...

    Text Solution

    |

  2. P Q R S is a trapezium having PS a n d Q R as parallel sides. A is a...

    Text Solution

    |

  3. A B C D is a parallelogram. P is the mid-point of A BdotB D\ a n d\...

    Text Solution

    |

  4. P is any point on base B C of A B C\ a n d\ D is the mid-point of...

    Text Solution

    |

  5. Two parallelograms are on equal bases and between the same parallels. ...

    Text Solution

    |

  6. A triangle and a parallelogram are on the same base and between the...

    Text Solution

    |

  7. Let A B C be a triangle of area 24sq. units and P Q R be the tri...

    Text Solution

    |

  8. The median of a triangle divides it into two congruent triangle ...

    Text Solution

    |

  9. In a A B C ,\ D ,\ E ,\ F are the mi-points of sides B C ,\ C A\ a...

    Text Solution

    |

  10. A B C D is a parallelogram. P is any point on C Ddot If a r\ ( D...

    Text Solution

    |

  11. The area of the figure formed by joining the mid-points of the adja...

    Text Solution

    |

  12. A ,\ B ,\ C ,\ D are mid-points of sides of a parallelogram P Q R Sd...

    Text Solution

    |

  13. The figure obtained by joining the mid-points of the adjacent sides...

    Text Solution

    |

  14. The mid points of the sides of a triangle A B C along with any of ...

    Text Solution

    |

  15. If A D is median of A B C and P is a point on A C such that a r...

    Text Solution

    |

  16. Medians of A B C intersect at G . If a r\ ( A B C)=27\ c m^2, then...

    Text Solution

    |

  17. In a A B C if D\ a n d\ E are mid-points of B C\ a n d\ A D respec...

    Text Solution

    |

  18. In Figure, ABCD is a parallelogram. If AB=12 c m , AE=7.5 cm , CF=15 c...

    Text Solution

    |

  19. In Figure, PQRS is a parallelogram. If X and Y are mid-points of PQ an...

    Text Solution

    |

  20. In Figure, ABCD and FECG are parallelograms equal in area. If ar (AQE)...

    Text Solution

    |