given,
AD=BD
BF=1/2 FC
CE=1/2AE
area of
ABC = 120 cm²
find
area of A DEF=?
Answers
In Δ ADE and Δ ABC,
∠ADE =∠ABC (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE ~ Δ ABC (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC
[In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4+DB) = 2/5
2.4 × 5 = 2(2.4+ DB)
12 = 4.8 + 2DB
12 - 4.8 = 2DB
7.2 = 2DB
DB = 7.2/2
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 × 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
Step-by-step explanation:
”
If AD = DB and DE is parallel to BC then..
Tri ADE is similar to ABC.
Area of ABC = H * 1/2 * BC ; ( Area of a Triangle is the Height X 1/2 the Base)
But we are given H * 1/2* BC = 40
BD = DA, So DE must be 1/2 of BC.
(Notes: Because AD/AB is 1/2 ; then DE/BC must also be 1/2 ; Likewise H of ADE is 1/2 of H of ABC; Similar Triangles)
Area of DAE then is H*1/2 * 1/4* BC (Notes; DE is 1/2 of BC, so half of DE is 1/4 of BC ).
Juggling we get; 1/4(H*1/2*BC)
But we are given H*1/2 * BC = 40 ; so we can substitute 40 for that in our equation… 1/4 ( 40 ) = Area of Triangle DAE.
Ergo Area of Triangle DAE = 1/4 * 40 …which is 10
Answer Area of DAE = 10 Sq units.
Hope that helps.
Supplement.
Consider the Square ABCD, and in it the Triangle ABC.