maths plse help me..
posted by sania .
ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT
1) ar(EGB) = 1/6 ar(ABCD)
2)ar(EFC) = 1/2 ar(EBF)
3) ar(EBG) = ar(EFC)
4) FIND WHAT PORTION OF THE ARE OF PARALLELOGRAM IS THE AREA OF EFG.

1)
height h of ABCD and EGB is the same
base of EGB = 1/3 AB
area(ABCD) = h*AB
area(EGB) = 1/2 h*(1/3 AB) = 1/6 h*AB
2)
base of EFC = 1/2 base of EBF
so area is 1/2 as well
3)
if g = altitude from AD to BC
area(EFC) = 1/2 * (2/3 g) * (1/3 BC) = 1/9 area(ABCD)
So, I get area(EFC) = 2/3 area(EBG)
Is there a typo here?
4)
area(EFG) = area(EGB)+area(EBF)+area(EFC)
= 1/6(ABCD)+2area(EFC)+area(EFC)
= 1/6(ABCD) + 3(1/9 ABCD)
= 1/2(ABCD)
Respond to this Question
Similar Questions

maths plse help me..
ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT 1) ar(EGB) = 1/6 ar(ABCD) 2)ar(EFC) = 1/2 ar(EBF) 3) ar(EBG) = ar(EFC) … 
maths plse help me..
ABCD ia a parallelogram whose diagonals intersecting at E. AC is produced to F such that CF=AE. Prove that ar(BDF)=ar(parallelogram ABCD) 
geometry
ABCD is a parallelogram. E is a point on AB such that 234×AE=EB. Let DE intersect AC at F. What is the ratio AC:AF? 
geometrY!
ABCD is a parallelogram. E is a point on AB such that 234×AE=EB. Let DE intersect AC at F. What is the ratio AC:AF? 
geometry!
ABCD is a parallelogram. E is a point on AB such that 234×AE=EB. Let DE intersect AC at F. What is the ratio AC:AF? 
maths(GEPMETRY)
ABCD is a parallelogram. E is a point on AB such that 234×AE=EB. Let DE intersect AC at F. What is the ratio AC:AF? 
geometry
ABCD is a parallelogram. Let C′ be a point on AC extended such that the length of AC′=1.2AC. Let D′ be on the segment BD such that the length of BD′=0.9BD. The ratio of the area of the quadrilateral ABC′D′ … 
maths
ABCD is a parallelogram. E is a point on DC extended, such that D and E are on opposite sides of BC. Let AE intersect BC and BD at F and G, respectively. If AG=180 and FG=108, what is EF? 
Geometry
ABCD is a parallelogram. P is a point on AB such that AP:AB = 1:4. Q is a point on CD such that DQ:DC = 1:3. AQ and DP intersect at R. Find the ratio AR:RQ and the ratio AR:AQ. Show work. 
Linear Relations MATHS
If A = (4,6) and B = (6,7), find: (a) the coordinates of the point P on the line segment AB such that AP:Pb = 3:1 (b) the coordinates of the point P on the line AB such that AP:AB = 3:1 and P is closer to point B than to point A