Link to the May 2017 Brain Puzzler Solution:
April’s Brain Puzzler
What is the area of the shaded region of the given 8 x 5 rectangle?
What is the area of the shaded region of the given 8 x 5 rectangle?
![[asy] size(6cm); defaultpen(fontsize(9pt)); draw((0,0)--(8,0)--(8,5)--(0,5)--cycle); filldraw((7,0)--(8,0)--(8,1)--(0,4)--(0,5)--(1,5)--cycle,gray(0.8)); label("$1$",(1/2,5),dir(90)); label("$7$",(9/2,5),dir(90)); label("$1$",(8,1/2),dir(0)); label("$4$",(8,3),dir(0)); label("$1$",(15/2,0),dir(270)); label("$7$",(7/2,0),dir(270)); label("$1$",(0,9/2),dir(180)); label("$4$",(0,2),dir(180)); [/asy]](https://latex.artofproblemsolving.com/9/5/f/95f8b885091c3cb0d7a2cb9325def6a059bfb982.png)
The area is 6.5 square units.
Using extra lines to break the shape into triangles is a great way to solve this problem.
https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_11
Math Confidence by Robin the Math Lady 