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
Zarrin [17]
2 years ago
15

The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nea

rest whole number, if necessary. 30 square units 60 square units 102 square units 120 square units

Mathematics
2 answers:
a_sh-v [17]2 years ago
7 0
Check the picture below.

so the rhombus has the diagonals of AC and BD, now keeping in mind that the diagonals bisect each, namely they cut each other in two equal halves, let's find the length of each.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad 
C(\stackrel{x_2}{6}~,~\stackrel{y_2}{8})\qquad \qquad 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{[6-(-4)]^2+[8-(-2)]^2}\implies AC=\sqrt{(6+4)^2+(8+2)^2}
\\\\\\
AC=\sqrt{10^2+10^2}\implies AC=\sqrt{10^2(2)}\implies \boxed{AC=10\sqrt{2}}\\\\
-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
B(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad 
D(\stackrel{x_2}{4}~,~\stackrel{y_2}{0})\qquad \qquad BD=\sqrt{[4-(-2)]^2+[0-6]^2}
\\\\\\
BD=\sqrt{(4+2)^2+(-6)^2}\implies BD=\sqrt{6^2+6^2}
\\\\\\
BD=\sqrt{6^2(2)}\implies \boxed{BD=6\sqrt{2}}

that simply means that each triangle has a side that is half of 10√2 and another side that's half of 6√2.

namely, each triangle has a "base" of 3√2, and a "height" of 5√2, keeping in mind that all triangles are congruent, then their area is,

\bf \stackrel{\textit{area of the four congruent triangles}}{4\left[ \cfrac{1}{2}(3\sqrt{2})(5\sqrt{2}) \right]\implies 4\left[ \cfrac{1}{2}(15\cdot (\sqrt{2})^2) \right]}\implies 4\left[ \cfrac{1}{2}(15\cdot 2) \right]
\\\\\\
4[15]\implies 60

ANEK [815]2 years ago
7 0

Answer:

The area of the rhombus is 60 square units

Step-by-step explanation:

You might be interested in
What is the word form of 872,403,159
OlgaM077 [116]

872,403,159 in word form is:

eight-hundred seventy-two million, four hundred three thousand, one hundred and fifty-nine.

hope this helps

7 0
2 years ago
Read 2 more answers
There's a pair of points (3,5), (x,15) and a slope of 2 how do I find x​
sergeinik [125]

You have the slope and you have two points, so you can use the slope equation to find x.

b=\frac{(y_2-y_1)}{(x_2-x_1)} \\2=\frac{(15-5)}{(x-3)} \\2(x-3)=(15-5)\\2x-6=10\\2x=16\\x=8

So your answer is x = 8.

8 0
3 years ago
Read 2 more answers
How many bases does a rectangular prism have?<br> one<br> two<br> three<br> four
kolezko [41]

Answer:

B. two

explanation:

i took the test

hope this helps. have a great day!!

7 0
3 years ago
Read 2 more answers
-20 + 4x = -6x<br> x = 5<br> x = -5<br> x = 2<br> x = -2
Cerrena [4.2K]

Answer:

x=2

Step-by-step explanation:

Hint use m a t h w a y. Its a algebra problem solver.

4 0
2 years ago
Read 2 more answers
Please help me answer this with the correct answer :)
Andru [333]

Answer:

A.

Step-by-step explanation:

Amber get $150 per week no matter wut and +$10 per tree sold so if she sells 5 trees she gets a total of $200

Jorge gets $25 per tree sold and an extra $75at the end of the week so 25(5)=125+75=200 so they both end up with $200 at the end of the week

4 0
3 years ago
Other questions:
  • Order the group of quadratic functions fro widest to narrowest graph Y= 6x sq Y = -4.5 sq y =-x
    13·1 answer
  • A certain electronics manufacturer found that the average cost C C to produce x DVD/Blu- ray players can be found using the equa
    6·1 answer
  • Which of the following have two congruent parallel bases ?
    15·2 answers
  • When cai traveled from New orleans,Louisiana to the Ozark mountains in Arkansas , the elevation changed from 7ft below sea level
    12·2 answers
  • Solve for x by finding the missing side of the triangle. Round your answer to the nearest tenth ​
    9·1 answer
  • The density of water is 1 gram per cm^3. An object floats in water if its density is
    13·1 answer
  • Solve for x please help me
    7·1 answer
  • 3) Graph y=-x2+3 <br> State the vertex and axis of symmetry
    8·2 answers
  • The lcm of 5 and 8 is??
    15·1 answer
  • A prince has arrived to rescue a princess standing in a tower balcony 18 meters up across a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!