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
Rus_ich [418]
3 years ago
12

Given: PRST is a square

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
5 0

Answer:

(1-\sqrt{2})a^2

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a

Thus,

MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a

Consider isosceles triangle MSC. In this triangle

MS=MC=(\sqrt{2}-1)a.

The area of this triangle is

A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}

Consider right triangle PTS. The area of this triangle is

A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2

You might be interested in
Suppose that the probability that your mail is delivered before 2pm is .90. What is the probability that your mail will be deliv
Elden [556K]
1. The probability that your mail is delivered before 2 pm is 0.9, so the probability that the mail is delivered at 2 pm or after 2 pm (so not before 2 pm) is 1-0.9=0.1.

Remark: 0.9=9/10=90/100=90%, and 0.1 is 10%

2. Probability of the mail being delivered before 2 pm for 2 consecutive days is 
\frac{90}{100}*  \frac{90}{100}= \frac{9}{10}*  \frac{9}{10}= \frac{81}{100}=0.81

3. take a look at the picture attached, the tree diagram is another method we could use. 

4 0
2 years ago
lisa has played in 6 soccer matches. Her brother josh has played in 18 soccer matches. lisa saay josh has played in 12 times as
Basile [38]

Answer:

Josh has played 12 matches more, not 12 times as many as her.

Step-by-step explanation:

Lisa said times, making the statement incorrect.

5 0
3 years ago
What song has a slower tempo??<br><br>A)Death bed<br><br>B)Godzilla
disa [49]
Death bed has slower tempo
7 0
2 years ago
What is the volume ?
slavikrds [6]

Answer:

I think the answer is 381.7

3 0
3 years ago
Read 2 more answers
Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x re
Veronika [31]

Answer:

The equations which represents the situation are

1) 2Y+X=5

2) 5X-Y=3

Step-by-step explanation:

<em>~Cornasha_Weeb</em>

3 0
2 years ago
Other questions:
  • 8 (3g+2)-3g=3 (5g-4)-2
    9·1 answer
  • Witch is longer 2 feet or 30 inches
    7·2 answers
  • Jenna created the graph below to represent the solution to the inequality Negative 6 less-than x.
    12·2 answers
  • What is 5292cm rounded to the nearest thousandth
    15·1 answer
  • Draw an area model to solve 774 divided by 3
    8·1 answer
  • Bart budgeted $285.75 each month for utilities. His utility bills this month were $130.50 for electric, and $240 for gas. How mu
    10·1 answer
  • Solve for x. PLEASE SHOW WORK AND HELP
    14·1 answer
  • 10a²+4= -186<br> Very easy quick points
    5·1 answer
  • 2b) if d = 1/2 what is t?
    8·1 answer
  • The slope indicates how fast y increases or decreases as x increases.<br> O True<br> O False
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!