Mathematics, 02.07.2020 14:01 elijahjacksonrp6z2o7

A square has a side that measures 2.75 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth. 94.99 units2 23.75 units2 9.62 units2 38.47 units2

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Answer from: sssudeegaming1943

The area of a circle with a circumference that equals the perimeter of the square is 9.62 units²

Step-by-step explanation:

The first thing we must do is find the perimeter of the square. In the problem, we are given that one of the side measurements of the square is 2.75 units. In order to find the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.

2.75 × 4 = 11

So, the perimeter of the square is 11 units. This number will also be the number for the circumference of the circle as mentioned in the problem. So, the circumference of the circle is 11 units. Now, we must find the radius of the circle so we can find the area. Let's use the formula for finding radius given the circumference.

$Radius = \frac{circumference}{2\pi}$

Now, let;s plug in 11 for the circumference because our circumference is 11 units.

$Radius=\frac{11}{2\pi}$

Multiply 2 by pi. We will use 3.14 in replacement of pi.

$Radius=\frac{11}{6.28}$

Now, divide.

Radius=1.75

So, our radius is 1.75 units. We can know use this number to find the area of the circle.

$Area=r^2\pi$

Plug in 1.75 for the radius.

$Area=(1.75)^2\pi$

Simplify the exponent.

$Area=(3.0625)\pi$

Multiply the numbers.

Area=9.61625

Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.

9.61625 = 9.62

So, the area of the circle is 9.62 units²

Answer from: Quest

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = $\frac{1}{2}$ (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

The figure below shows a triangle with vertices a and b on a circle and vertex c outside it. side ac

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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A square has a side that measures 2.75 units. What is the area of a circle with a circumference that...