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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 t

Roman55 [17]

The total area of the figure is 139.20 square centimeters

Areas

The area of a shape is the amount of space it occupies

<h3>Composite figure</h3>

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

7 0

2 years ago

I need the expression

V125BC [204]

Answer:

-7( 8n - m )

- 7 × 8n + 7× m

-56n + 7m

7 0

3 years ago

Read 2 more answers

Mr. Patel’s house is 1,850 ft 2 . He tiles 30% of the house on the first day. He tiles 185 ft 2 each day after that. How many mo

Black_prince [1.1K]

Step-by-step explanation:

Tile A $9.75

Tile BTiles are $11 per tile if fewer than 50 tiles are purchased. For 50 or more tiles, tiles are $9.50 per tile.

Tiles are purchased by the box

Tile C There are 24 tiles per box. Each box is $185.

3 0

3 years ago

Read 2 more answers

Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 3

Rama09 [41]

Answer:

The probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

Step-by-step explanation:

Let X = number of household owns a sports car.

The probability of X is, P (X) = p = 0.07.

Then the random variable X follows a Binomial distribution with n = 3 and p = 0.07.

The probability function of a binomial distribution is:

$P(X=x) = {n\choose x}p^{x}[1-p]^{n-x}\\$

Compute the probability that of the 3 households randomly selected at least 1 owns a sports car:

$P(X\geq 1)=1-P(X$

Thus, the probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

4 0

3 years ago

Find the distance between 2 - 4 and 6 + i

saveliy_v [14]

Answer:

Step-by-step explanation:

hello :

let : Z1 = 2-4i Z2 = 6+i

the distance between Z1 and Z2 is :

/Z2 - Z1 / = /(6+i)-(2-4i)/ =/4+5i/ = √(4²+5²) =√41

3 0

3 years ago