Question

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.

Answer 1

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:

$A_1 = \sqrt{\frac{3s^2}{4}}$

Where:

$s = 6$ --- the length of each toothpick

The area of the rectangle is then represented as:

$A_2 =3s \times s$

$A_2 =3s^2$

So, the total area of the figure is:

$Total = 6A_1 + A_2$

This gives

$Total =6 \times \sqrt{\frac{3s^2}{4}} + 3s^2$

Substitute 6 for s

$Total =6 \times \sqrt{\frac{3(6)^2}{4}} + 3(6)^2$

$Total =6 \times \sqrt{27} + 108$

$Total =6 \times 5.20+ 108$

$Total =139.20$

Hence, the total area of the figure is 139.20 square centimeters

Read more about areas at:

brainly.com/question/21135654