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Stells [14]
3 years ago
11

I don’t understand...

Mathematics
1 answer:
Katarina [22]3 years ago
8 0

Answer:

A

when you simplify the equation you get A

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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
a_sh-v [17]
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}&#10;\\\\&#10;A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad &#10;C(\stackrel{x_2}{6}~,~\stackrel{y_2}{8})\qquad \qquad &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;AC=\sqrt{[6-(-4)]^2+[8-(-2)]^2}\implies AC=\sqrt{(6+4)^2+(8+2)^2}&#10;\\\\\\&#10;AC=\sqrt{10^2+10^2}\implies AC=\sqrt{10^2(2)}\implies \boxed{AC=10\sqrt{2}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;B(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad &#10;D(\stackrel{x_2}{4}~,~\stackrel{y_2}{0})\qquad \qquad BD=\sqrt{[4-(-2)]^2+[0-6]^2}&#10;\\\\\\&#10;BD=\sqrt{(4+2)^2+(-6)^2}\implies BD=\sqrt{6^2+6^2}&#10;\\\\\\&#10;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]&#10;\\\\\\&#10;4[15]\implies 60

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