1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leno4ka [110]
2 years ago
14

NO LINKS!!! Find the area of the shaded figure shown. Part 3.#16 & 17. Show work please.

Mathematics
2 answers:
RideAnS [48]2 years ago
4 0

#17

Area of rectangle

  • 20(21)
  • 420m²

Diameter of circle

  • √21²+20²
  • √400+441
  • √841
  • 29m

Radius=29/2=14.5m

Area

  • π(14.5)²
  • 660m²(approx)

Area of shaded region

  • 660-420
  • 240m²

#17

Area of circle

  • π(16/2)²
  • 64π
  • 200.96ft²

Side of square(Let it be s)

Use Pythagorean theorem

  • s²+s²=16²
  • 2s²=16²
  • s²=256/2
  • s²=128

Area of square

  • s²
  • 128ft²

Area of shaded region

  • 200.96-128
  • 72.96ft²
trapecia [35]2 years ago
4 0

Answer:

16)  240.52 m²  (2 dp)

17)  73.06 ft²  (2 dp)

Step-by-step explanation:

<h3><u>Question 16</u></h3>

To calculate the shaded area, subtract the area of the rectangle from the area of the circle.  (We know it's a rectangle since the opposite sides are equal in length - marked by dashes).

\begin{aligned}\textsf{Area of a rectangle}& =\sf width \times length\\\implies \sf A& = \sf 20 \times 21\\& = \sf 420\:\:m^2\end{aligned}

To find the area of the circle, first find the radius.

From inspection of the diagram, the diagonal of the rectangle is the diameter of the circle. Therefore, the radius is half the diagonal.

To find the length of the diagonal, use Pythagoras' Theorem:

\begin{aligned}\sf a^2+b^2 & = \sf c^2\\\implies 20^2+21^2 & = \sf c^2\\\sf c^2 & = 841\\\sf c & =\sqrt{841}\\\sf c & = 29\end{aligned}

Therefore:

\begin{aligned}\implies \sf radius & = \sf \dfrac{1}{2}c\\\\& = \sf \dfrac{1}{2}(29)\\\\& = \sf1 4.5\:m\end{aligned}

\begin{aligned}\textsf{Area of a circle} & = \sf \pi r^2\\\implies \sf A & = \sf \pi (14.5)^2\\& = \sf 210.25\pi \:\:m^2\end{aligned}

Finally:

\begin{aligned}\textsf{Shaded area} & = \textsf{area of circle}-\textsf{area of rectangle}\\& = \sf 210.25 \pi - 420\\& = \sf 240.52\:\:m^2\:(2\:d.p.)\end{aligned}

<h3><u>Question 11</u></h3>

To calculate the shaded area, subtract the area of the square from the area of the circle.  (We know it's a square as the side lengths are equal - marked by one dash on each side length).

\begin{aligned}\textsf{Area of a circle} & = \sf \pi r^2\\\implies \sf A & = \sf \pi \left(\dfrac{16}{2}\right)^2\\& = \sf 64\pi \:\:ft^2\end{aligned}

To find the area of the square, first find the side length using Pythagoras' Theorem:

\begin{aligned}\sf a^2+b^2 & = \sf c^2\\\implies 2a^2 & = \sf 16^2\\\sf a^2 & = 128\\\sf a & =\sqrt{128}\\\sf a & = 8\sqrt{2}\:\:\sf ft\end{aligned}

\begin{aligned}\textsf{Area of a square} & = \sf a2\\\implies \sf A & = \sf (8\sqrt{2})^2\\& = \sf 128 \:\:ft^2\end{aligned}

Finally:

\begin{aligned}\textsf{Shaded area} & = \textsf{area of circle}-\textsf{area of square}\\& = \sf 64 \pi - 128\\& = \sf 73.06\:\:ft^2\:(2\:d.p.)\end{aligned}

You might be interested in
PLS HELP. The cost of printing a flyer to spread knowledge of an organization that you run is a flat rate of $9 plus $0.05 per c
myrzilka [38]
U would need to spend about 100-500 dollars on copies
5 0
3 years ago
Read 2 more answers
Gary is buying a $1,250 computer on the installment plan you makes a down payment on of $150 she has to make monthly payments of
Nataliya [291]
1250-150=1100
2 1/2 years = 30 months
30*48.25 = 1447.5 - 1100 = $<span>347.5 is you Answer</span>
3 0
3 years ago
Read 2 more answers
What is the measure of \thetaθtheta in radians?<br> radians<br> \qquad
Evgesh-ka [11]

Answer:

\dfrac{\theta\pi}{180^\circ} $ radians

Step-by-step explanation:

To convert \theta from degrees to radians, you simply multiply the value of \theta  by \frac{\pi}{180^\circ}

Take for an example,

To convert 45 degrees to radians,

45^\circ=45^\circ X \dfrac{\pi}{180^\circ} \\=\dfrac{1}{4}\pi$  radians

8 0
3 years ago
If a number is increased by 20% then the number is 24 find the number
trasher [3.6K]

Answer:

20

Step-by-step explanation:

  • x+20%=24
  • x+x*20/100=24
  • x+0.2x=24
  • 1.2x=24
  • x=24/1.2
  • x=20
4 0
3 years ago
Mb= d + h Solve equation for b
juin [17]

Answer:

b =  (d + h)/M

Step-by-step explanation:

Mb= d + h

Divide each side by M

Mb/ M= (d + h)/M

b =  (d + h)/M

8 0
3 years ago
Read 2 more answers
Other questions:
  • Shane pays $2568 per year in tuition. How much should he budget monthly for it? (Points : 3) $107 $156 $214 $228
    9·2 answers
  • A car sells for $5000 and loses 1/10 of its value each year.
    9·1 answer
  • 1846<br><br> What is the smallest and largest?
    12·1 answer
  • Solve the following equation by completing the square. Enter your answers from smallest to largest. Round your answer you answer
    10·1 answer
  • Solve the value of s<br><br> (s-4)+58=180
    8·2 answers
  • Which of the following is a solution for the inequality 2x &lt; 9?
    6·2 answers
  • PLS HELP 100 POINTS!!!!!!!!!!!!!!! A female orca eats 125 kilograms of marine animals each day. At this rate, how many days will
    14·1 answer
  • Solve for x.<br> 4 + 2x = 10
    9·1 answer
  • Solve the system by substitution.<br> -2x-10y=-2<br> -4y=x
    10·1 answer
  • Hello! I don't understand how to do this question Triangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!