Question

In triangle ABC, AD = DB , DE is parallel to BC, and the area of triangle ABC is 40 units. What is the area of triangle ADE ?

Answer 1

Answer:

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.