ABCD is a rectangle, E is the mid-point of AD. A point F on EC such that CF : FE = 1 : 2. If ar(ABCD) = 180 cm2, then find the ar(ΔBDF).
Answers
Answer:
Here I applied coordinate geometry concept. Find each coordinate in form of parameter"a" then find corresponding coordinate then find height and base of triangle BDF by find distance formula from line.
Then area=1/2*base*height
Given : ABCD is a rectangle, E is the mid-point of AD. A point F on EC such that CF : FE = 1 : 2 , ar(ABCD) = 180 cm²
To find : ar(ΔBDF).
Solution:
Let say A = ( 0 , 0 ) & D = ( 0 , 2a)
=> E = (0 , a) ( mid point of AD)
=> AD = 2a
Area of ABCD = 180 = AD * BC
=> 180 = 2a * BC
=> BC = 90/a
Hence B = ( 90/a , 0)
C = (90/a , 2a)
C = (90/a , 2a) , E = (0 , a)
CF : FE = 1 : 2
=> F = ( 1 * 0 + 2 * 90/a)/(1 + 2) , ( 1 * a + 2 * 2a)/(1 + 2)
=> F = (60/a , 5a/3)
B = ( 90/a , 0) , D = (0 , 2a) , F = (60/a , 5a/3)
area of Δ BDF
= (1/2) | (90/a) ( 2a - 5a/3) + 0(5a/3 - 0) + (60/a)(0 - 2a) |
= (1/2) | 180 - 150 + 0 - 120 |
= (1/2) | - 90 |
= 90/2
= 45
ar(ΔBDF). = 45 cm²
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