## anonymous one year ago square ABCD has sides of length 12 units each. Points W, X, Y, and Z lie on sides AB, BC, CD, and DA, respectively, so that AW = 1/2 AB, BX = 1/2 BC, CY = 1/3 CD, and AZ = 1/4 DA. What is the area of the quadrilateral WXYZ?

1. anonymous

2. mathmate

|dw:1440268312680:dw| Area of square, As= (12x)^2 = 144x^2 Calculate the total area of the 4 triangles at the four corners (A=bh/2) At=6x*6x+6x*4x+8x*9x+3x*6x=.... Subtract At from As to get the area of the quadrilateral. Aq=As-At

3. mathmate

Correction: At=(6x*6x+6x*4x+8x*9x+3x*6x)/2=....

4. anonymous

????? I'm just in Junior high...

5. anonymous

@mathmate

6. anonymous

7. anonymous

IDK

8. mathmate

If you are confused with the 12x and 144x^2 (which is a general case), set x=1, so the side of the square is 12 units (as given in the question.

9. mathmate

|dw:1440269114269:dw|

10. mathmate

Then calculate area of the four corner triangles: |dw:1440269166364:dw| The area of the square is 12*12=144 u^2 Area of the quadrilateral is 144-(sum of the areas of the four triangles). Can you take it from here?

11. anonymous

So if each sides are 12. The area of the rectangle is 144. then add all of the triangles together subtract that from 144.