In given figure, E divides diagonal AC of rectangle ABCD in 1: 3 ratio. F and G are midpoints of ED and EC respectively then find the ar(ΔEFG)/ar(ABCD)
Answers
Given : E divides diagonal AC of rectangle ABCD in 1: 3 ratio. F and G are midpoints of ED and EC respectively
To Find : ar(ΔEFG)/ar(ABCD)
Solution:
Diagonal Divided area of rectangle in 2 Equal area
Hence
Area Δ ACD = (1/2) Area of Rectangle ABCD
E divides diagonal AC of rectangle ABCD in 1: 3 ratio
=> Area Δ ECD = (3/(1 + 3) ) * Area Δ ACD
=> Area Δ ECD = (3/4 ) * Area Δ ACD
=> Area Δ ECD = (3/4 ) * (1/2) Area of Rectangle ABCD
=> Area Δ ECD = (3/8 ) Area of Rectangle ABCD
Now F and G are mid points of ED and EC
Hence ar(ΔEFG) = (1/2²) Area Δ ECD
=> ar(ΔEFG) = (1/4) Area Δ ECD
=> ar(ΔEFG) = (1/4) (3/8 ) Area of Rectangle ABCD
=> ar(ΔEFG) / Area of Rectangle ABCD = 3/32
ar(ΔEFG)/ar(ABCD) = 3/32
Learn More:
Ratio of area of 2 similar triangles are 2:3. Area of the larger triangle is
brainly.in/question/7877543
if triangle abc- triangle def area of triangle abc is 64 square ...
brainly.in/question/14594418
Three triangles are marked out of a bigger triangle at the three ...
brainly.in/question/8018381