Question

Please answer this correctly

Answer 1

Answer:

$10.71 yd$

Step-by-step explanation:

First let's find the radius of the quarter circle.

$area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r$

Now let's find the arc length of this quarter circle.

$\frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd$

Now let's find the perimeter$perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd$

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Answer 2

Answer:

10.71 yd

Step-by-step explanation:

The formula of an area of a circle:

$A=\pi r^2$

r - radius

The formula of an area of a quarter circle:

$A=\dfrac{1}{4}\pi r^2$

We have the area of a quarter circle:

$A=7.065\ yd^2$

Substitute to the formula and solve for r :

$\dfrac{1}{4}\pi r^2=7.065$     multiply both sides by 4

$4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26$

Use 3.14 for π

$3.14r^2=28.26$            divide both sides by 3.14

$\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}$

The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.

The formula of a circumference of a circle:

$C=2\pi r$

The formula of a quarter of a cicrumference of a circle:

$L=\dfrac{1}{4}\cdot2\pi r$

Substitute

$L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi$

Use 3.14 for π

$L=1.5(3.14)=4.71\ yd$

The perimeter of a quarter circle:

$P=4.71+2(3)=4.71+6=10.71\ yd$