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
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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