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The area of a triangle is half the produ...

The area of a triangle is half the product of any of its sides and the corresponding altitude. GIVEN : A ` A B C` in which `A L` is the altitude to the side `B Cdot` TO PROVE : `a r( A B C)=1/2(B CxxA L)` CONSTRUCTION : Through `C` and `A` draw `C D B A` and `A D B C` respectively, intersecting each other at `Ddot`

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`"BC is parallel to AD"`
`"AB is parallel to CD"->"ABCDis a parallelogram and AC is a diagonal "`
`ar(/_\ABC)=1/2"(ar of parallelogram ABCD)"`
`" "=1/2(BCxxAL)`
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RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
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  2. Prove that If each diagonal of a quadrilateral separates it into two...

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  3. The area of a triangle is half the product of any of its sides and t...

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  4. Triangles A B C and +DBC are on the same base B C with A, D on opposit...

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  5. If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O ...

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

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  7. Prove that the diagonals of quadrilateral A B C D ,A C and B D interse...

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  8. X Y isa line parallel to side B C of A B CdotB E A and C F A B meet...

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  9. In Figure, A B C D is a trapezium in which A B D C and D C=40c m and ...

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

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

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  12. A B C D is a parallelogram whose diagonals A C and B D intersect at Od...

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  13. A point D is taken on the side B C of a A B C such that B D=2d Cdot P...

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  14. In Figure, D , E are points on sides A B and A C respectively of A B ...

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

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  16. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

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

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  18. The area of a trapezium is half the product of its height and the s...

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  19. Parallelogram A B C D and rectangle A B E F have the same base A B and...

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  20. O is any point on the diagonal B D of the parallelogram A B C Ddot Pro...

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