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
leva [86]
3 years ago
11

Show that the area of triangle DEF is 11 cm2.​

Mathematics
1 answer:
dedylja [7]3 years ago
5 0

9514 1404 393

Explanation:

The length CD can be found from the Pythagorean theorem.

  CF² + CD² = DF²

  2² + CD² = (2√10)²

  CD² = 40 -4 = 36

  CD = √36 = 6

From here, any of several methods could be used to find the area of ΔDEF.

One of them is to subtract the areas of the triangles that are not ΔDEF from the area of the rectangle ABCD.

  area ABCD = bh = (6 cm)(5 cm) = 30 cm²

  area ΔADE = 1/2bh = 1/2(4 cm)(5 cm) = 10 cm²

  area ΔBEF = 1/2bh = 1/2(2 cm)(3 cm) = 3 cm²

  area ΔCDF = 1/2bh = 1/2(6 cm)(2 cm) = 6 cm²

Then the area of interest is ...

  area ΔDEF = area ABCD -area ΔADE -area ΔBEF -area ΔCDF

  area ΔDEF = (30 -10 -3 -6) cm²

  area ΔDEF = 11 cm²

__

<em>Alternate solution</em>

If we define A as the origin of a coordinate system, then the coordinates of the vertices of ΔDEF are ...

  D(0, 5), E(4, 0), F(6, 3)

The area can be computed as half the absolute value of the sum of the determinants of 2×2 matrices consisting of adjacent points.

  A=\dfrac{1}{2}\left|\left|\begin{array}{cc}0&5\\4&0\end{array}\right|+\left|\begin{array}{cc}4&0\\6&3\end{array}\right|+\left|\begin{array}{cc}6&3\\0&5\end{array}\right| \right|\\\\=\dfrac{1}{2}|(0-20)+(12-0)+(30-0)|=\dfrac{1}{2}(22) = \boxed{11}

_____

<em>Additional comment</em>

The solution using coordinates is effectively equivalent to the computation of the area of trapezoid ABFD, less the areas of triangles EBF and AED.

You might be interested in
a cog company produces 20 cogs a day, 4 of which are defective. Find the probability of selecting 4 cogs from the 20 produced wh
Simora [160]

Answer:

1/4845

Step-by-step explanation:

The probability of selecting a defective cog first is

1/5

The second cog is

3/19

The third cog is

1/9

And the fourth cog is

1/17

Multiplying these together we get

1/5 * 3/19* 1/9 * 1/17  = 1/4845

7 0
3 years ago
Describe the pattern in the following sequence and list the next three terms:
balu736 [363]

Answer:

4×2=8

8×2=16

16×2=32

32×2=<em>6</em><em>4</em>

<em>6</em><em>4</em><em>×</em><em>2</em><em>=</em><em>1</em><em>2</em><em>8</em>

<em>1</em><em>2</em><em>8</em><em>×</em><em>2</em><em>=</em><em>2</em><em>5</em><em>6</em>

<em>I </em><em>HOPE</em><em> THIS</em><em> HELPS</em><em> U</em>

5 0
3 years ago
Read 2 more answers
Lori has 25 new stamps but she already has 15 old ones how many does she have in total
KonstantinChe [14]
She would have a total of 40 stamps. 
7 0
3 years ago
C<br> What is the missing hypotenuse length? *<br> х<br> 6<br> 8
4vir4ik [10]

Step-by-step explanation:

By Pythagoras' Theorem, 6^2 + 8^2 = x^2.

x^2 = 36 + 64 = 100, x = 10.

7 0
3 years ago
Which of the following is equal to the rational expression when x -2 or -1? x^2-4/(x+2)(x+1)
Orlov [11]

Answer:

(x+2)(x+1)

Step-by-step explanation:

Assuming im interpreting this correctly, it should be (x+2)(x+1), since if you plug in -2 and -1, it will give you 0, which is the answer.

8 0
3 years ago
Other questions:
  • Is 60% greater than 5/9
    5·1 answer
  • I need help to change the subject of the formula to W
    10·1 answer
  • Please show me how to do this!!
    12·1 answer
  • If the volume of the pyramid shown is 108 inches cubed, what is the area of its base? A pyramid with a height of 8 inches. 4 inc
    12·1 answer
  • The jazz band has m members to raise money for a tour each member sold raffle tickets
    15·1 answer
  • Hailey is a salesperson who sells computers at an electronics store. She makes a base pay amount of $100 per day regardless of s
    14·2 answers
  • PLS I WILL GIVE U BRAINLIEST ANSWER PLS HELP!
    12·2 answers
  • PLZ HURRY IT'S URGENT!!!
    9·2 answers
  • First answer gets brainliest
    9·2 answers
  • I don't know how to solve this at all, i just need some help on how to figure it out. Thanks!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!