Question

In the parallelogram ABCD, BQ = 2QC and P is
any point on AD. If the area of the parallelogram
ABCD is 48 cm, find the area of APQC.
​

Answer 1

Answer:

area of triangle pQC is 8 unit square

Step-by-step explanation:

let ,

base of parallelogram be x

AD = BC = x __( 1 ) opposite sides of parallelogram are congruent

height of parallelogram be y

AD parallel to BC

therefore, AB =PQ=PC=DC =y ___ (2 )

BQ = 2QC ___(3) given

BC = BQ + QC ___ B-Q-C

area of parallelogram = BASE × HEIGHT

48 = BC × DC

48 = 2QC+QC × y ___ from 2 and 3

48 = 3QC ×y

48/3y = QC

QC = 16/ y _____(4)

area of triangle PQC = 1/2 × BASE × HEIGHT

= 1/2 ×QC × y __ from 2

= 1/2 × 16/y × y __ from 4

= 8 unit sq