1. In the diagram, the area of rectangle $EFGH$ is $\dfrac 14$ of the area of unit square $ABCD.$ What is the area of quadrilateral $AFCH$ in square units?

2. Two long strips of paper are each 2 inches wide, and they overlap so that the angle between the strips is $30^{\circ}$. What is the number of square inches in the area of the parallelogram formed by the overlap?

3. As shown in the diagram, $\overline{PQ}$ is the median of trapezoid $ABCD,$ where $AB=25$ inches and $CD=36$ inches. Find $XY$ in inches.

4. In the Reflecting Ball Game, a ball can be launched from points 1, 2, 3, 4, 5 or 6 in the direction shown. When a ball hits a side of rectangle $ABCD$, it bounces at a $90^{\circ}$ angle back into the playing field. The path of the ball ends when it hits corner point $A$, $B$, $C$, or $D$. The path for starting point 5 is shown in the diagram. Each of the $15$ non-overlapping squares of the playing field has an area of $2$ square centimeters. What is the length of the longest possible path for a ball launched from a starting point?

qwertyytrewq Mar 8, 2021

#3**+2 **

**1.)**

The quadrilateral has the entire EFGH that is 1/4 unit^{2 }(given)

AND 1/2 of the the remaining 3/4 is included in the quad

ABCD is given as unit square

1/4 + 1/2 * 3/4 = 5/8 unit^{2 }= AFCH area

^{Please only post one question at a time.....you are more likely to get all of them answered if posted seperately. }

ElectricPavlov Mar 8, 2021