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fenix001 [56]
3 years ago
5

Need help finding the area of the shaded region. Round to the nearest tenth. Need help ASAP

Mathematics
2 answers:
Sergio [31]3 years ago
8 0

Answer:   294.4 m²

<u>Step-by-step explanation:</u>

Separate the shaded region into two parts:

  1. The section containing the central angle of 230° (360° - 130°)
  2. The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)

1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3

2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1

Area of shaded region = Area of (1) + Area of (2)

                                      =    247.3     +      47.1

                                      =               294.4

expeople1 [14]3 years ago
5 0

Answer:

294.36

Step-by-step explanation:

Find the area of the entire circle.

Subtract out the area of a sector with 130 degrees for the central angle.

Add the area of the isosceles triangle with an apex angle of 130 degrees.

Area of The entire circle

Area = pi * r^2

Area = 3.14 * 11.1^2

Area = 386.88 m^2

Area of the sector with 130 degrees for a central angle

Area_130 = (130/360) * pi * r^2

Area_130 = (130/360) * 3.14* 11.1^2

Area_130 = 139.71

Area of the triangle

1/2 central angle = 130/2 = 65

Bisect the apex angle so that each half = 65 degrees.

Sin(65) = opposite / hypotenuse

Sin(65) = Opposite / 11.1

11.1 * sin(65) = opposite

opposite = 10.06

This is 1/2 the base so the base = 2*10.06 = 20.12

The height of the triangle is found by cos(65) = adjacent/hypotenuse

hypotenuse = 11.1

Cos(65) = adjacent / hypotenuse

adjacent = hypotenuse * cos(65)

adjacent = 4.69 This is the height of the triangle.

Area of the triangle = 1/2 * 20.12 * 4.69

Area of the triangle = 47.19 m^2

Area of the Shaded Area

Area of entire circle - area of sector + area of triangle

=386.88 - 139.71 + 47.19

=294.36

Note

The area of the triangle could be done using Area = 1/2 * 11.1^2 * (2*sin(65)*cos(65) = 1/2 * 11.1^2 * sin(130) = 47.2 but you may not know all the math to do the area this way.

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John put away 36 of 48 shirts in his closet. Don has 84 shirts. If he put away the same percent, how many shirts did Don put in
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Answer:

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Step-by-step explanation:

John's percentage:

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we know Don has 84 shirts so we say

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Alex_Xolod [135]

Question 14, Part (i)

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A+B+C+D = 360

A+90+C+90 = 360

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Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.

==================================================

Question 14, Part (ii)

Let

x = measure of angle 1

y = measure of angle 2

z = measure of angle 3

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Note that angles 1 and 2 are adjacent to form a straight line, so we can say

x+y = 180

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We have the two equations x+y = 180 and y+z = 180 to form this system of equations

\begin{cases}x+y = 180\\y+z = 180\end{cases}

Which is really the same as this system

\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.

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