SOLUTION: In a square ABCD, X is the midpoint of AB and Y is the midpoint of BC. What percent of the area of square ABCD is the area of triangle XYD?

Algebra ->  Parallelograms -> SOLUTION: In a square ABCD, X is the midpoint of AB and Y is the midpoint of BC. What percent of the area of square ABCD is the area of triangle XYD?      Log On


   

Question 1019684: In a square ABCD, X is the midpoint of AB and Y is the midpoint of BC. What percent of the area of square ABCD is the area of triangle XYD?
Answer by ikleyn(52858) About Me  (Show Source):
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In a square ABCD, X is the midpoint of AB and Y is the midpoint of BC. What percent of the area of square ABCD is the area of triangle XYD?
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1. Make a sketch.

2. The area of the triangle AXD is 1%2F4 of the area of the square.

3. The area of the triangle YCD is 1%2F4 of the area of the square.

4. The area of the triangle XBY is 1%2F8 of the area of the square.

5. The area of the three listed triangles is 

   1%2F4+%2B+1%2F4+%2B+1%2F8 = 5%2F8

   of the area of the square.

6. Therefore, the area of your triangle XYD is 1+-+5%2F8 = 3%2F8 of the area of the square.

7. Hence, the percentage under the question is %283%2F8%29%2A100 = . . . (?).

   Please calculate it yourself.