Question

Question 6:
4 points
ABCD is a square, E and F are respectively the
mid-points of BC and CD. If R is the mid-point of
EF and ar(AAFR) = 46 cm2, then ar(AAER) is
(1) 42 cm
(2) 32 cm
(3) 46 cm2
(4) 52 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)