9. Calculate the area of the pentagon in the figure below.

7 answers
Question:

9. Calculate the area of the pentagon in the figure below.

[tex]9. Calculate the area of the pentagon in the figure below.[/tex]


Answers

1) 76.5 cm²

               2) 35.07 m²

Step-by-step explanation:

1) The area of a trapezoid is A = (B + b)h/2

A = (11.5+6.5).8.5/2 = 18 . 8.5/2 = 153/2 = 76.5 cm²

2) For the pentagon, as it is a regular pentagon, we can divide it into 2 shapes. A equilateral triangle and a square.

Area of the square = l² = 9² = 81 m²

Area of a equilateral trinagle = l²√3/4 = 9²√3/4 = 81√3/42 = 81 . 1.73/2 = 140.3/4 = 35.07 m²

132.5 cm²

Step-by-step explanation:

Given the ratio of 2 similar figures = a : b, then the

ratio of areas = a² : b²

Here the ratio of sides = 5 : 9, thus

ratio of areas = 5² : 9² = 25 : 81

Let x be the area of the smaller pentagon then by proportion

[tex]\frac{x}{25}[/tex] = [tex]\frac{429.3}{81}[/tex] ( cross- multiply )

81x = 10732.5 ( divide both sides by 81 )

x = 132.5

Area of smaller pentagon is 132.5 cm²

139 cm squared

The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

Given

1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.

2) Regular pentagon PENTA with side lengths 9 m

Find

The area of each figure, rounded to the nearest integer

Solution

1) The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

The are the area should be 86

Y=3x+1 so the first one
[tex]Me answer this question question 2) select the function that matches the graph[/tex]

+1,000)=g7e=mc2-g=7 because if you know algebra you should know g=7 to get your answer

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