Mathematics: Patrick is building a patio in the shape of a decagon with a radius of 12 feet. To determine the amount of cement needed, he must first find the area.

Step-by-step explanation: where =Hope that helps :)...

Patrick is building a patio in the shape of a decagon

BreBreDoeCCx

18.01.2022

The area of the Patrick's building is 2340.22 ft^2 .

Step-by-step explanation:

Shape of the Patrick's building = Decagon

In the figure attached:

Radius of the decagon = r = 12 feet

Side of the decagon = a

Angle AOB = 36°

Using trigonometric ratio is triangle AOC :

AO = r = 12 feet

AC = $\frac{a}{2}=0.5a$

$\tan \theta=\frac{Perpendicular}{base}$

$\tan 36^o=\frac{0.5a}{12 feet}$

$a=\frac{\tan 36^o\times 12 feet}{0.5}=17.44 feet$

Area of decagon :

$A=\frac{5}{2}a^2\times \sqrt{5+2\sqrt{5}}$

$A=\frac{5}{2}(17.44 ft)^2\times \sqrt{5+2\sqrt{5}}$

A=2340.22 ft^2

The area of the Patrick's building is 2340.22 ft^2 .

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popa60

23.04.2020

Step-by-step explanation:

$y^{2/5\\}$ where $y\neq 0$

$y^{m/n\\}$ = $\sqrt[n\\]{y^{m} }$

$\sqrt[5\\]{y^{2} }$

Hope that helps :)

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