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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?

 Mar 8, 2021
 #1
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Only ask one question at a time.

 Mar 8, 2021
 #2
avatar+54 
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Then can you answer at least 1 instead of complaining?

 Mar 8, 2021
 #3
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1.)  

         The quadrilateral has the entire EFGH      that is 1/4   unit2    (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 unit2       = AFCH area

 

 

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

 Mar 8, 2021

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