Flip made a flag for her boat. She took a red square. She then put a white triangular piece of material over the red square. Her working sketch is shown below.
If P and Q are the midpoints of the original square, what fraction of the square did the white flag cover?
Solution
In the rectangle ABRP, PB is a diagonal. Hence area of triangle APB = area of triangle PBR. Since rectangle ABPR is 1/2 of square, the area of triangle APB is 1/4 of square.
Similarly the area of triangle QBC is 1/4 square of square. Now triangle PDQ is 1/2 of area of square PXQD. This square is 1/4 of the original square. Hence triangle PDQ has area 1/8 of square.
So the white triangle covers 1 - 1/4 - 1/4 - 1/8 = 1 - 5/8 = 3/8 of the square.