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Question

(i)Write a property of diagonals of parallelogram.

(ii)ABCD is a parallelogram in which CD is produced to P.DC =6 cm and height BQ = 4 cm. Find the area of \(\Delta APB\)


4cm

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Solution

(i) Diagonals of parallelograms bisects each other.

(ii)Theorem used:

Area of triangle is half the area of parallelogram, if both are on same base and between the same parallels.

From the given figure:

AB||CD (ABCD is a parallelogram)

AB=CD=6cm (given)

Altitude BQ=4cm (given)

ΔABP and parallelogram ABCD are on same base and between the same parallels.

Area of ΔAPB=12× Area of ABCD

Area of ABCD = Base×Altitude

Area of ABCD = 6×4=24 cm2

Area of ΔAPB=12×Area of ABCD

Area of ΔAPB=12×24

Area of ΔAPB=12 cm2


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