Question

The figure below shows AB = 2 units and BD = 5 units.



If the area of triangle ADE is 70 square units, what is the area of the trapezoid BCED?

58.80 square units

5.71 square units

7.53 square units

64.29 square units

Answer 1

7.53??

Answer 2

im wondering if the cow is going a ratio solution

Answer 3

9i have no clue

Answer 4

no its not 7.53
you have to solve this using proportions...and that ratio of areas = ratio of sides squared
for triangle ADE, length of side is 7 and Area is 70
for smaller triangle ABC, length of side is 2, Area is A
\[\frac{A}{70} = (\frac{2}{7})^{2}\]
then the trapezoid is the difference in the areas

Answer 5

i knew it had to be something along those lines ;)

Answer 6

im so lost

Answer 7

yep :)
is there a better way?

Answer 8

if we take a general stab it this, and determine the relationship that exists between similar triangles and their areas i get this
\[A_{t1}=\frac{bh}{2}\]
\[A_{t2}=\frac{n^2bh}{2}\]

Answer 9

i just read that if you cant solve a problem in more than one way; than you cant solve the problem ;)

Answer 10

@TiaW
the 2 triangles are similar, thats why i can use the proportion
first solve for Area of smaller triangle, solve for A in the equation i posted

Answer 11

since we know more of the larger triangle; lets use that as firsties

7:2 such that 1: 2/7 is the proportion of sides lengths

so the area im thinking would be (2/7)^2 to be proportional

Answer 12

would that be 70?

Answer 13

the area? no the area of triangle ADE is 70
area of triangle ABC is much smaller

Answer 14

i dont know how to solve that

Answer 15

@amistre64
good job....but thats exactly what i did

Answer 16

what is (2/7)^2 ?

Answer 17

4/49

Answer 18

good, so now you have
\[\frac{A}{70} = \frac{4}{49}\]
how do you move the 70 to other side, so is A is by itself?

Answer 19

280a=28
a=10

Answer 20

but
10/70 does not equal 4/49

how did you get 280a = 28 ?

Answer 21

... in my defense, what i did may seem exactly like what you did, but i did it with one brain cell tied behind my cerebral cortex ;)

Answer 22

opps.
49A=280
a=5.71

Answer 23

haha...it was a better explanation , i will give you that :)

Answer 24

very good :)
now subtract that from 70 to get area of trapezoid

Answer 25

70-5.71=64.29?

Answer 26

yep

Answer 27

thank u bunches