Construct a convex quadrilateral and then a quadrilateral similar to it whose area is three-fourths of the area of the original quadrilateral.

2. Hello, thamathkid1729!

I already solved this at another site . . .

3. Hello, everyone!

This is the long and clunky solution I posted elsewhere . . .

whose area is three-fourths of the area of the original quadrilateral.

Suppose the original quadrilateral has sides $\displaystyle a,b,c,d.$
The smaller quadratilateral has sides multiplied by a factor of $\displaystyle \frac{\sqrt{3}}{2}.$

Construct an equilateral triangle with side 1.
Contruct an altitude; its length is $\displaystyle \frac{\sqrt{3}}{2}$
(I'll leave the proof to you.)

On a line, mark off points $\displaystyle A,\,B,\,C,\,\text{ where }AB \,=\,1,\:BC \,=\,\frac{\sqrt{3}}{2}$

Code:
      o-----o----o
A     B    C

From $\displaystyle \,A$, draw a line to the upper-right.

Code:
                            *
*
*
*
*
*
*
*
*
*
*
o-----o----o
A     B    C

On that line, mark off $\displaystyle AP \,=\,a$

Code:
                            *
*
*
*
P  *
o
*
a  *
*
*
*
o-----o----o
A     B    C

Draw line segment $\displaystyle BP.$

Code:
                            *
*
*
*
P  *
o
*/
a  * /
*  /
*   /
*    /
o-----o----o
A     B    C

From $\displaystyle \,C$ construct $\displaystyle CQ\,\parallel\, BP$

Code:
                            o Q
*/
* /
*  /
P  *   /
o    /
a  */    /
* /    /
*  /    /
*   /    /
*    /    /
o-----o----o
A     B    C

Then: $\displaystyle PQ \:=\:\frac{\sqrt{3}}{2}\,a \:=\:a'$

Repeat the process with side $\displaystyle \,b$ and find $\displaystyle b'.$

With that information, you can complete the construction.

Code:
                    a
* * * * * * *
*  a'    *     *
*           *     *
* b'        d' *     * d
b  *                 *     *
*          c'        *     *
* * * * * * * * * * * * *     *
*                                *
* * * * * * * * * * * * * * * * * * *
c

Note that: .$\displaystyle c'\parallel c\,\text{ and }\,d'\parallel d.$