Question

Question 5:
4 points
ABCD is a parallelogram and BC is produced to a
point Q such that AD = CQ. If AQ intersects DC
at P and ar(ABPC) = 24 cm2, then ar(ADPQ) is
(1) 32 cm2
(2) 24 cm2
(3) 28 cm2
(4) 36 cm2
​

Answer 1

Step-by-step explanation:

GivenLABCD is a square.E and F are the midpoints of BC and CD and R is the midpoint of EF

Proof:Consider △ABE and △ADF

We know that BC=DC(all sides of a square are equal.)

⇒

2

BC

=

2

DC

⇒EB=DF(since E and F are midpoints of BC and CD)

∠ABE=∠ADF=90

∘

(All angles in a square are right angles)

AB=AD(All sides in a square are equal)

∴ by SAS criterion, △ABE≅△ADF

Hence,AE=AF by C.P.C.T

⇒, R is the midpoint of EF

AR is the median of the triangle AEF

Since median divides the triangle into two triangles of equal areas,ar(△AER)=ar(△AFR)