Can someone explain to me why this is the correct answer? I am familiar with finding the area of both parallelograms and triangles, but I just can't seem to understand why this is the answer.

Question

anonymous · Answer

attachment

janu16 · Answer

sinA = h/16 = 6/10 
h = 6*16/10 = 96/10 = 9.6 ==> answer

janu16 · Answer

do you understand?

anonymous · Answer

To be honest, no. Can you draw a diagram?

mathmale · Answer

janu16:  Please state your assumptions.  Did you, for example, assume that two triangles in this illustration are SIMILAR?   Where is your angle A in "sinA = h/16 = 6/10"     Please explain your solution further.

mathmale · Answer

Why delete that comment?  It looked very helpful to me.

janu16 · Answer

really?

janu16 · Answer

The answer will be much easier to explain once I label the points. 

Let A, B, C, and D be the bottom left, bottom right, top right, and top left vertices (in this order) of the quadrilateral that looks like a parallelogram; in fact I will need to assume that ABCD is a parallelogram or else there would not be enough information to solve the problem. 

In ABCD, let the altitude from point D to the base AB intersect this base at point E. Let F be the vertex of the right angle of the upper right triangle. I will need to assume that A, D, and F are in a straight line or else there would not be enough information to solve the problem. 

We're given the lengths DE = 6, CD = 16, and BC = 10. We need to find FC = h. 

Solution: 

Since I'm assuming ABCD is a parallelogram, AD = BC = 10 and AB is parallel to CD. Furthermore, since I'm assuming that A, D, and F are in a straight line, corresponding angles DAE and CDF are congruent. Because, in addition, right angles AED and DFC are congruent, AA similarity implies that triangles ADE and DCF are similar. 

Therefore, DE/AD = CF/DC; 6/10 = h/16; h = 16(6/10) = 9.6 units.

mathmale · Answer

Whew.  Glad you still have it.

janu16 · Answer

i cant draw it cuase the mouse is too shaky @TayTay23 but i gave a explanation

anonymous · Answer

Okay thanks I'm reading through it now

janu16 · Answer

alright

mathmale · Answer

Please work together until the problem becomes clear for TayTay.