+0

# In trapezoiectively. The legs of the trapezoid are extended beyond A and B to meet at

0
170
2
+1364

In trapezoid ABCD the lengths of the bases AB and CD are 8 and 17 respectively. The legs of the trapezoid are extended beyond A  and B to meet at point . What is the ratio of the area of triangle EAB  to the area of trapezoid ABCD? Express your answer as a common fraction.

tertre  May 27, 2017
Sort:

#1
+91436
+2

Hi Tetre,

The word trapezoid means different things in different countries, could you plase give a definition that we should use?

I'll just tell what I think you mean.

AB and DC are parallel.

This means that AEB and DEC are similar triangles

so

the ratio of the height of ABE and DEC will be   8:17

so  Area of  AEB = 0.5*8*8k       and area of DEC = 0.5*17* 17k

and area of  ABCD = 0.5*17* 17k  -   0.5*8*8k

ratio of the area of triangle EAB  to the area of trapezoid ABCD

$$=\frac{0.5*8*8k}{0.5*17*17k\;-\;0.5*8*8k}\\ =\frac{8*8k}{17*17k\;-\;8*8k}\\ =\frac{8*8}{289\;-\;64}\\ =\frac{64}{225}\\$$

Melody  May 27, 2017
#2
+80910
+1

Since the two triangles created are similar, each dimension of the larger triangle created will be  (17/8)  that of the smaller triangle

Call h the height of the smaller triangle......so its   area  =  (1/2)*8*h  =  4h  (1)

And the area of the larger triangle  = (1/2)* 17 * (17/8) h   =   (289 / 16)h    (2)

So  the area  of the trapezoid  =  (2) - (1)   =  (289/16) h - 4h   =  [ 289 - 64 ] / 16 * h =

[225 / 16] h

So.....the ratio of the smaller triangle to the trapezoid  =  [4h] /  ( [ 225/ 16] h )  =  64 / 225

Just as Melody found....!!!!

CPhill  May 27, 2017

### 19 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details