Question

# ABCD is a parallelogram and P is the midpoint of AB. If ar(APCD) = 36cm^{2} , find ar(ABC).

Hint:

### Given , P is the midpoint of AB ;APCD form a trapezium as AP // DC

So , find the area of trapezium and equate it with the given value .

Now , find the ar(ABC).

## The correct answer is: 24 cm2

### Ans :- 24 sq.cm

Explanation :-

Step 1:-Find area of APCD

let length of AB be 2a the DC= AB(opposites sides of parallelogram are equal)

As p is mid point of AB ; AP = a

As AP // DC ;In quadrilateral if one pair of parllelsides exits then it is trapezium.

So area of APCD =

Step 2:- Find area of ABC

Area of triangle ABC = ½ base AB × height h

Area of ABC = ½×(2a)×(h) = ha

ha = 24

Therefore , the area of triangle ABC = 24 sq.centimeters

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