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
Solve the following -1/2x(8x +4)
antoniya [11.8K]

Combine like terms to get -4x^2-2x

3 0
3 years ago
If my rounded number is 9.7 what could the original number have been​
castortr0y [4]

Answer:

9.65-9.74

Those numbers and anything between them.

3 0
2 years ago
Lauren has 43 flowers she has 16 fewer flowers than gabriel how many flower does gabriel have
WARRIOR [948]

Answer:

Step-by-step explanation:

Gabrielhs 59 flowers because 43 + 16= 59.

7 0
2 years ago
Read 2 more answers
A cylinder has a diameter of 8 inches and a volume of 1287 cubic inches. What is the height of
fredd [130]

Answer:

25.62

Step-by-step explanation:

the answer is rounded and pi was 3.14 to solve this

8 0
3 years ago
Stan The Boyz<br>Stream Stealer
pentagon [3]
Ummmmmm whatttt I’m confuseddd
5 0
3 years ago
Read 2 more answers
Other questions:
  • The volume of a can of chicken broth that had a diameter of 7.5 Centimeters and a heighten 11 centimeters. Round to the nearest
    6·2 answers
  • I need help with these
    5·1 answer
  • A builder is buying property to build new houses. The sizes of the lots are 1 2 , 1 3 , 1 6 , 1 2 , 1 6 , 1 2 , 1 6 , 1 2 , 1 3
    8·1 answer
  • What is 40 over 72 in simplest form
    5·2 answers
  • What are the coordinates of the vertex of the function f(x) = x2 - 12x + 5?
    8·1 answer
  • Ann is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
    14·2 answers
  • Pls help pls help do anything u want ,but pls help
    6·1 answer
  • 6.105x 10^8/3.7x10^3
    8·1 answer
  • Solve the formula for V<br><br> D=m/V <br><br> V=
    15·1 answer
  • What is the value of u ?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!