Problem setup:
The shape is way too complicated by itself, so I cut the shape into 5 different parts.
Please refer to the attached image or my answer will not make much sense.
Shape 1:
This is a triangle. The base is 3 and the height is 2. Thus, the area is:
[tex]A=\dfrac{1}{2}*3*2[/tex]
[tex]=3[/tex]
Shape 1 has an area of 3 square units.
Shape 2:
This shape is also a triangle. The base is 4 and the height is 2. Thus, the area is:
[tex]A=\dfrac{1}{2}*4*2[/tex]
[tex]=4[/tex]
Shape 2 has an area of 4 square units.
Shape 3:
This a unit square (the side lengths are 1).
Thus, Shape 3 has an area of 1 square unit.
Shape 4:
This shape is a rectangle. The base is 3 and the height is 4. Thus, the area is:
[tex]A=3*4[/tex]
[tex]=12[/tex]
Shape 4 has an area of 12 square units.
Shape 5:
This shape is also a rectangle. The base is 4 and the height is 2. Thus, the area is:
[tex]A=4*2[/tex]
[tex]=8[/tex]
Shape 5 has an area of 8 square units.
Total shape:
Add the areas of all 5 shapes to find the area of the shaded figure.
[tex]A=3+4+1+12+8[/tex]
[tex]=26[/tex]
The figure has a total area of 26 square units.
Side notes:
There is a way to solve this problem by only dividing this into only 3 different shapes, can you figure it out?
Let me know if you need a hint or any clarifications, thanks!
~ Padoru
