Chapter 9. Areas of Parallelograms and Triangles

EXERCISE 9.1

1. Which of the following figures lie on the same base and between the same parallels. In such a case , write the common base and the two parallels .

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Solution:  (i) Parallelogram ABCD and triangle DPC lie on the same base DC and between the same parallels DC and AB . So, the common base is DC and two parallels are DC and AB .

(ii) Parallelogram PQRS and trapezium MNRS lie on the same base SR . but different parallels .

(iii) Parallelogram PQRS and triangle QTR lie on the same base QR and between the same parallels QR and PS . So, the common base is QR and two parallels are QR and PS .

(iv) Parallelogram ABCD and triangle PRQ lie on the same base BC . but different parallels .

(v)  Parallelogram ABCD and parallelogram APCD  lie on the same base AD and between the same parallels AD and BQ . So, the common base is AD and two parallels are AD and BQ .

(vi) Parallelogram PQRS and parallelogram ABCD do not lie on the same base AD and between the same parallel PQ and SR .

                                                                     EXERCISE 9.2
1. In Fig. 9.15, ABCD is a parallelogram, AE⊥DC and CF⊥AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Solution:  Given, AB = 16 cm, AE = 8 cm and CF = 10 cm .

ABCD is a parallelogram .

So,  AD = BC   and AB = DC .

Since, ABCD is a parallelogram and  AE⊥DC ,then

arABCD=AE×DC………i

Again , ABCD is a parallelogram and  CF⊥AD ,then

 
arABCD=AD×CF………ii

From (i) and (ii) , we get

AE×DC=AD×CF

⇒AE×AB=AD×CF

⇒8×16=AD×10

⇒AD=8×1610cm

⇒AD=12810 cm

⇒AD=12.8 cm