Question

find the area of the rhombus if the vertices are (3,0),(4,5),(-1,4) and (-2,-1)taken in order
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Answer 1

=√(-2-4)^2+(-1-5)^2

=√(-6)^2+(-6)^2

=√36+36

=√72

6√2

AC=√(-1-3)^2+(4-0)^2

=√(-4)^2+(4)^2

=√16+16

=√32

4√2

area of rhombus =1/2×product is sides

1/2×AC×BD

1/2×4√2×6√2

=24 sq.units

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Answer 2

Answer:

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

ABCD IS A RHOMBUS

=> AREA OF RHOMBUS ==> 1/2 * AC * BD

=> DISTANCE B/W AC

=> AC² = (3+1)²+(0-4)²

=> AC² = 16 + 16

=> AC² = 32

=> AC = √32 ==> 4√2 UNIT

NOW, DISTANCE BETWEEN BD

=> BD² = (4+2)²+(5+1)²

=> BD² = 36+36

=> BD = √72

=> BD = 6√2 CM

AREA OF RHOMBUS ==> 1/2×AC×BD

=> 1/2×4√2×6√2

=> 2√2 × 6√2

=> 24 CM

AREA = 24 CM