Question

If the area of triangle ADE is 50 square units, what is the area of the trapezoid BCED?

Answer 1

use the idea of conguent triangles

Answer 2

congruent*

Answer 3

Ok so you know that the area of triangle ADE is 50, and the lengths of line segment AB and BD. So, like myko said, use the idea of congruent angles. So here's how you do it. Since triangle ADE is similar to triangle ABC, we have to find the height of triangle ADE then the height of triangle ABC.
So here's how it's set up
Area of triangle=50
bh1/2=50
Now remember, we're finding the height, h. So the b, base, would be 10 because thats the length of segment AD, which was the sum of segment AB and BD.
10h1/2=50
Now simplify that by multiplying 2 of both sides, 1/2 on the left side gets canceled out while 50 becomes 100.
10h=100
Then divide both sides by 10 to isolate the h in order to find the height
h=10
The height of triangle ADE is 10. Now to find the height of triangle ABC. We know that the base is 4, so here's what you do, set up proportions since both triangles are similar.
10/10=4/x
Now you can do this, cross multiply and find x, the height. 10 times 4 is 40 and 10 times x is 10x.
10x=40
Now divide both sides by 10 to isolate your x
x=4
Now you have your height of triangle ABC. Now find the area of that triangle and subtract it from the area of triangle ADE.
(4)(4)1/2=x
16 1/2=x or 16/2
8=x
The area is 8, subtract it from the area of ADE, 50 and you get 42.
Hope that helps.