Question

What is the area of this figure?

Answer 1

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:

$A=\dfrac{1}{2}*3*2$

$=3$

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:

$A=\dfrac{1}{2}*4*2$

$=4$

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:

$A=3*4$

$=12$

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:

$A=4*2$

$=8$

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.

$A=3+4+1+12+8$

$=26$

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