How to get the shaded region of the rectangle?

Hint:

enter image description here

  • there are eight small red triangles all with the same area

  • six of them are shaded


The area of hatched region of the rectangle is the area of the rectangle minus the sum of the areas of the right triangles $BEF$ and $DGH$. Now if you glue these triangles along their hypotenuses, you obtain a rectangle with dimensions half the dimensions of the big rectangle, hence with area equal to ¼ area of the big rectangle.

Hence the required area is ¾ big area, i.e. $\color{red}{48}$.


enter image description here

If you notice that if you combine two right triangles then they occupy the area of $\dfrac14$ of the total area.

So, the area of the shaded region is $=64-\dfrac14(64)=64-16=48$

Tags:

Geometry

Recent Posts