Question

f̲i̲n̲d̲ t̲h̲e̲ a̲r̲e̲a̲ o̲f̲ a̲ r̲h̲o̲m̲b̲u̲s̲ w̲h̲o̲s̲e̲ v̲e̲r̲t̲i̲c̲e̲s̲ t̲a̲k̲e̲n̲ i̲n̲ o̲r̲d̲e̲r̲ t̲o̲ p̲o̲i̲n̲t̲s̲ (3,0);(4,5);(-1,4) a̲n̲d̲ (-2,-1)

Answer 1

Hey !!!^_^

Here is your answer

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Let A(0,3) , B(4,5) , C(-1 ,4) , D(-2 , -1)

Area of rhombus =

1/2 × product of its diagonal ..

In RHOMBUS ABCD ,, AC and BD are rhe diagonal ...

Using Distance formula ..

$\sqrt {(x2 - x1) {}^{2} + ( y2 - y1}) {}^{2} \\ \\ ac = \sqrt{ {( - 1 - 3)}^{2} +( {4 - 0})^{2} } \\ \\ ac = \sqrt{32} \\ \\ ac = 4 \sqrt{2} \\ \\ now.... \: \\ \\ bd = \sqrt{ {(4 - ( - 2))}^{2} + {(5 - 1)}^{2} } \\ \\ bd = \sqrt{52} \\ \\ bd = 2 \sqrt{13} \\ \\ area \: of \: rhombus \: \\ \\ \frac{1}{2} \times 2 \sqrt{13} \times 4 \sqrt{2} \\ \\ 4 \sqrt{26} \: sq \: unit$
Therefore the area of rhombus is 4√26 sq. unit

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I HOPE IT WILL HELP YOU

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Answer 2

Answer is 4root 62................