SOLUTION: A triangular piece of glass (XYC) is cut from a rectangular pane (ABCD). Points X and Y are the midpoints of two sides of the rectangular pane. What fraction of the area ABCD is XY

Question 608760: A triangular piece of glass (XYC) is cut from a rectangular pane (ABCD). Points X and Y are the midpoints of two sides of the rectangular pane. What fraction of the area ABCD is XYC?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there,
.
Do you know which sides of the rectangular pane contain the points X and Y? The fraction will differ depending upon where X and Y are located.
.
Here is one solution to your problem. If the points X and Y are on different sides of the rectangle with respect to point C the fraction may be different. However the solution method is the same.
.
Make a drawing to follow along.
Let X be the midpoint of side AB
Let Y be the midpoint of side AD
.
Draw triangle XYC.
.
Let W be the width of the rectangle. So W=AB=CD.
Let L be the length of the rectangle. So L=AD=BC.
.
The area of the rectangle is W*L.
.
Now find the areas of the three right triangles and subtract those area from the rectangle area. This is the area of triangle XYC.
.
Triangle AXY:
base = 1/2 * W
height = 1/2 * L
area:

.
Triangle YCD:
base= W
height = 1/2 * L
area:

.
Triangle XBC:
base = 1/2 * W
height = L
area:

.
Area of triangle XYC

.
Fraction of triangle area over rectangle area:

.
Hope this helps! Feel free to email via gmail if you have questions,
Ms.Figgy
math.in.the.vortex@gmail.com
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