The total area of the figure is 139.20 square centimeters
Areas
The area of a shape is the amount of space it occupies
Composite figure
The figure (see attachment) is a composite figure, and the total area is the sum of the areas of each shape that makes up the complete figure
The shape has 6 equilateral triangles, each of which has an area of:
[tex]A_1 = \sqrt{\frac{3s^2}{4}}[/tex]
Where:
[tex]s = 6[/tex] --- the length of each toothpick
The area of the rectangle is then represented as:
[tex]A_2 =3s \times s[/tex]
[tex]A_2 =3s^2[/tex]
So, the total area of the figure is:
[tex]Total = 6A_1 + A_2[/tex]
This gives
[tex]Total =6 \times \sqrt{\frac{3s^2}{4}} + 3s^2[/tex]
Substitute 6 for s
[tex]Total =6 \times \sqrt{\frac{3(6)^2}{4}} + 3(6)^2[/tex]
[tex]Total =6 \times \sqrt{27} + 108[/tex]
[tex]Total =6 \times 5.20+ 108[/tex]
[tex]Total =139.20[/tex]
Hence, the total area of the figure is 139.20 square centimeters
Read more about areas at:
https://brainly.com/question/21135654
