Question

If A (0.5), B(6, 11 ) and C( 10,7) are the vertices of a triangle ABC, D and E
are the mid-points of AB and AC respectively. Then find the area of triangle ADE.​

Answer 1

Given : A (0.5), B(6, 11 ) and C( 10,7) are the vertices of a triangle ABC, D and E  are the mid-points of AB and AC respectively

To find : area of triangle ADE.​

Solution:

A ( 0 , 5)  , B ( 6 , 11)  & C (10 , 7)

Area of Δ ABC

= (1/2) | 0 (11 - 7) + 6( 7 - 5) + 10(5 - 11) |

= (1/2) | 0 + 12 - 60 |

= (1/2) | - 48|

= 48/2

= 24

Area of ΔABC =  ( 2² )Area of ΔADE   as D& E are mid points so BC = 2DE & ΔABC ≈ ΔADE

=>  Area of ΔADE  = 24/4

=> Area of ΔADE  = 6

Another method

D = (0 + 6)/2, (5 + 11)/2 = 3 , 8

E = (0  + 10)/2 , (5 + 7)/2 = 5 , 6

A ( 0 , 5)  , D ( 3 , 8)  & E (5 , 6)

Area = (1/2) | 0 (8 - 6) + 3(6 - 5)  + 5(5 - 8)|

= (1/2) | 0  + 3 - 15|

= (1/2) | - 12 |

= 12/2

= 6

Area of ΔADE  = 6 sq units

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