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Twenty toothpicks, each 6 cm long, form a figure consisting of six equilateral triangles and a rectangle as shown. What is the total area of the figure? Express your answer as a decimal to the nearest hundredth.

Sagot :

MrRoyal

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

View image MrRoyal
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