Q7 of 77 Page 15

In Fig. 15.80, ABCD is a trapezium in which AB||DC. Prove that ar(Δ AOD) = ar(Δ BOC).

Given that,

ABCD is a trapezium with AB ‖ DC


To prove: Area ( = Area (


Proof: Since,


ΔABC and ABD are on the same base AB and between the same parallels AB and DC


Therefore,


Area (Δ ABC) = Area (Δ ABD)


Area (Δ ABC) – Area (Δ AOB) = Area (ΔABD) – Area (Δ AOB)


Area (Δ AOD) = Area (Δ BOC)


Hence, proved


More from this chapter

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5

In Fig. 15.78, ABCD is a trapezium in which AB=7 cm, AD=BC=5 cm, DC=x cm, and distance between AB and DC is 4 cm. Find the value of x and area of trapezium ABCD.

 6

In Fig. 15.79, OCDE is a rectangle inscribed in a quadrilateral of a circle of radium 10 cm. If OE=2 , find the area of the rectangle.

 8

In Fig. 15.81, ABCD and CDEF are parallelograms. Prove that

ar(Δ ADE) = ar(Δ BCF).


 9

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:

ar(Δ APB) × ar(Δ CPD) = ar(Δ APD) × ar(Δ BPC).