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
nexus9112 [7]
2 years ago
13

Find the area of the composite figure.

Mathematics
1 answer:
Roman55 [17]2 years ago
3 0

Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

<u>According to the Figure Given:</u>

Total Horizontal Distance = 14 in

Length = 6 in

<u>To Find :</u>

The Area of the composite figure

<u>Solution:</u>

Firstly we need to find the area of Rectangular part.

So We know that,

\boxed{ \rm \: Area  \:  of \:  Rectangle = Length×Breadth}

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

\boxed{\rm \: Breadth = total  \: distance - Radius}

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

\longrightarrow\rm \: Length \:  of \:  the  \: circle = Radius

  • Since Length = 6 in ;

\longrightarrow \rm \: 6 \: in   = radius

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

  • Total Horizontal Distance= 14
  • Radius = 6

\longrightarrow\rm \: Breadth = 14-6

\longrightarrow\rm \: Breadth = 8 \: in

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

  • Length = 6
  • Breadth = 8

\longrightarrow\rm \: Area \:  of  \: Rectangle = 6 \times 8

\longrightarrow \rm \: Area \:  of  \: Rectangle = 48 \: in {}^{2}

Then, We need to find the area of Quarter circle :

We know that,

\boxed{\rm Area_{(Quarter \; Circle) }  = \cfrac{\pi{r} {}^{2} }{4}}

Now Substitute their values:

  • r = radius = 6
  • π = 3.14

\longrightarrow\rm Area_{(Quarter \; Circle) } =  \cfrac{3.14 \times 6 {}^{2} }{4}

Solve it.

\longrightarrow\rm Area_{(Quarter \; Circle) } =  \cfrac{3.14 \times 36}{4}

\longrightarrow\rm Area_{(Quarter \; Circle) } =  \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4}

\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9

\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \:  {in}^{2}

Now we can Find out the total Area of composite figure:

We know that,

\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}

So Substitute their values:

  • \rm Area_{(rectangle)} = 48
  • \rm Area_{(Quarter Circle)} = 28.26

\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26

Solve it.

\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}}

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

\rule{225pt}{2pt}

I hope this helps!

You might be interested in
The ratio of fiction to nonfiction books in a classroom library is 2 to 3 . If there are 24 books nonfiction books in the classr
worty [1.4K]

Answer:

<h2>16</h2>

Step-by-step explanation:

Given the ratio of fiction to nonfiction books in a classroom library is 2 to 3, then the total ratio of both books will be 2+3 = 5. If there are 24 books non fiction books in the library, to get the amount of fictionbooks that are there we will follow the following steps.

First we will calculate the total number of books in the shelf;

3/5 * Total number of books = total non fiction books

3/5 * Total number of books = 24

3*Total number of books = 5*24

3*Total number of books = 120

Total number of books = 120/3

Total number of books = 40

Therefore there are 40 total of books on the shelf.

Total number of fiction books = 2/5 * 40

Total number of fiction books = 2* 8

Total number of fiction books = 16 books

<em>Hence there are 16 fiction books on the shelf.</em>

3 0
3 years ago
6 • 14 - (9 + 8) 2 =
Nataly [62]

Answer:

50

Step-by-step explanation:

For this question you would follow the BIDMAS rule - (Brackets, Indices, Division, Multiplication, Addition, Subtraction.)

The first thing in this question you need to solve it (9 + 8)

we do this because, when we follow BIDMAS, the first rule is brackets

so, 9 + 8 = 17

The second step is to multiply, as this rule is second,

so, 17 x 2 = 34

Our final step is to solve the last bit, which is 6 x 14

and we know that 6 x 14 = 84

So now that we have 84 and 34, we need to subtract the two numbers as shown,

84 - 34 = 50

And this is how you get the answer 50

i hope this has helped you, please comment if you did not understand it and i will explain it in another way : )

4 0
3 years ago
Read 2 more answers
Divide 71/9 2/34 <br><br>A. 21/4 <br>B. 23/4<br>C. 41/4<br>D. 413/16<br><br><br>HELLPPPPPP ​
ozzi

Answer:

A 5.25, B 5.75, C 10.25, D 25.8125

Step-by-step explanation:

8 0
3 years ago
Equation of a line parallel to y=2x+3 with a y intercept of 7
asambeis [7]

Answer:

y = 2x + 7

Step-by-step explanation:

For a straight line to be parallel to another it needs to have the same gradient. Therefore 2x stays the same and we just change out our y-intercept.

4 0
2 years ago
Read 2 more answers
A rectangular rug has a perimeter of 460 meters. The width of the rug is five meters more than 4 times the length. Find the
Paladinen [302]

Answer:

Length = 45 m

Width = 185 m

Step-by-step explanation:

Given:

Perimeter of rectangular rug = 460 m

width of the rug is five meters more than 4 times the length

To find:

Width and length of rug = ?

Solution:

Let the length = l m

As per given statement,

Width = 4l+5 m

Formula for perimeter of a rectangle = 2\times (Length +Width)

460=2\times (l+4l+5)\\\Rightarrow 230 = 5l+5\\\Rightarrow l = \dfrac{225}{5} = 45\ m

Width = 4l+5 m

Width = 4\times 45+5 = 185\ m

So, the answer is:

<em>Length = 45 m</em>

<em>Width = 185 m</em>

<em></em>

6 0
3 years ago
Other questions:
  • Find the probability that the person is frequently or occasionally involved in charity work.
    12·1 answer
  • A rectangle has a length five more than twice the width. If the perimeter is 22 units find the width and length
    14·1 answer
  • How would -9-(-5) look like as an addition problem?
    7·2 answers
  • Naomi has earned $51 mowing lawns the past two days. She worked 1 1/2 hours yesterday and 2 3/4 hours today. If Naomi is paid th
    15·1 answer
  • Determine whether Y= 2x^2 -1 is a linear equation. If so , write the equation in standard form. If Not PLEASE Explain?​
    14·1 answer
  • ****BRAINLIEST GOES TO THE FIRST CORRECT ANSWER****
    7·1 answer
  • PLEASE HELP
    6·1 answer
  • What is the area of the figure shown below?
    5·2 answers
  • I need help with this problem
    15·1 answer
  • To find x-intercept, substitute ____<br> in for ______<br> Ex: y = 3x + 3
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!