The mid-points of the sides of a square are joined to the opposite vertices -

Dev

Feb 2020
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0
UK
Any help with the attached question will be very much appreciated thanks.Untitled.jpg
 

skipjack

Forum Staff
Dec 2006
21,481
2,470
The shapes surrounding the central quadrilateral can be rearranged (by rotating each triangle about its "tip" by 90 degrees clockwise) to form four quadrilaterals of the same size and shape as the central quadrilateral, so the required area is a fifth of the area of the outer square.
 
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skeeter

Math Team
Jul 2011
3,363
1,854
Texas
The shapes surrounding the central quadrilateral can be rearranged (by rotating each triangle about its "tip" by 90 degrees clockwise) to form four quadrilaterals of the same size and shape as the central quadrilateral, so the required area is a fifth of the area of the outer square.
yep ...

area_square.jpg