Polygon Y has an area of 11 square units. Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it Polygon Z

Answers

The area of polygon Z is 99 square units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> area of polygon Z

y ----> area of polygon Y

z^{2}=\frac{x}{y}

we have

z=3

y=11\ units^2

substitute and solve for x

3^{2}=\frac{x}{11}

x=9(11)\\x=99\ units^2

so

The area of polygon Z is 9 times the area of polygon Y

The area of polygon Z is 99 square units

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It is the side...polygon is the base height

\mathbb{SOLUTION:}

Refer  to the figure

\\

\mathsf{\theta=\dfrac{360}{n}}

n = number of sides = 5

\mathsf{\theta=\dfrac{360}{5}}

\mathsf{\theta=72^\circ}

\mathsf{\dfrac{\theta}{2}=36^\circ}

\\

Consider ΔABO:

\mathsf{tan\left(\dfrac{\theta}{2}\right)=\dfrac{\dfrac{s}{2}}{r}}

\mathsf{tan\left(\dfrac{\theta}{2}\right)=\dfrac{s}{2r}}

\mathsf{\tan(36^\circ)=\dfrac{s}{2(6)}}

\mathsf{s=12tan(36^\circ)}

\mathsf{s=8.718510336 \: \: units}

\\

The area of a regular polygon is given by the equation:

\mathsf{A=\dfrac{ns^2}{4tan\left(\dfrac{180}{n}\right)}}

where:

s = length of side of the polygon

n = number of sides

\mathsf{A=\dfrac{(5)(8.718510336)^2}{4tan\left(\dfrac{180}{5}\right)}}

\mathsf{A=130.777655 \: \: sq. \: units}

\\

The area of the polygon can also be computed using the area of triangle ABO and multiplying it by 5.

\mathsf{A_{\Delta}=\dfrac{1}{2}(6)(8.718510336)}

\mathsf{A_{\Delta}=26.15553101}

\mathsf{A=5A_{\Delta}=5(26.15553101)}

\mathsf{A=130.777655 \: \: sq \: units}

\\

\mathbb{ANSWER:}

\boxed{\mathsf{s=8.718510336 \: \: units}}

\boxed{\mathsf{A=130.777655 \: \: sq. \: units}}


A circle of radius 6 is inscribed in a 5 sided regular polygon. Find the length of one side of the p
99 units²

Step-by-step explanation:

Polygon Y has an area of 11 square units. i.e the area of original figure is 11 square units.

Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it polygon Z.

So the original figure is expanded 3 times. So its sides and apothem will be 3 times of the previous length.

As we know that,

Area of the polygon = 1/2 × perimeter × apethom

As along with the sides, the perimeter and apethom also increases 3 times. Hence, the area will increase 3×3 = 9 times.

Therefore, the area of the polygon Z will be,

= 11 × 9

= 99 units²

#CarryOnLearning



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