Question

Area of quadrilateral ACDE is 36 cm^2, B is the mid-point of AC. Find the area of triangle ABE if
AC||DE and BE||DC
A) 10 cm^2
B) 9 cm^2
C) 12 cm^2
D) can't be determined ​

Answer 1

Answer:

• Draw diagonal EC
• Since we know, area of triangle is half the area of parallelogram sharing same base and between same parallel lines, area of ∆ECD = 0.5 • ar( parallelogram ACDE ) = 18 sq. cm
• Also, this area equals the area of ∆AEC which implies, ar( ∆ACE ) = 18 sq. cm

Now,

• We know, median divides the ∆ in two equal parts which implies ar( ∆ABE ) = 0.5 • ar( ∆ACE ) = 9 sq. cm

So, your answer is B)