Find the area of a rhombus if its vertices are (3,0), (4, 5), (-1, 4) and (-2, -1) taken in order.
Answers
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Step-by-step explanation:
Let The Point of Rhombus Be A,B,C and D.
A=(3,0) =( x1,y1 )
B= (4,5) =( x2,y2 )
C =(-1,4) =( x3,y3 )
D= (-2,-1)=( x4,y4 )
By Distance Formula
AB =√(x1 - x2)^2 + (y1- y2)^2
= √(3-5)^2 + (0 - 5)^2
= √(-2)^2 + (-5)^2
= √4+ 25
AB = √29
AB =BC=CD=AD =√29 ......(SIDE OF RHOMBUS ARE EQUAL)
Now Let Us Find The Diagonal.
By Distance Formula
AC =√(x1-x3)^2+(y1-y3)^2
AC=√(3-(-1) )^2 + (0-4)
AC=√(4)^2 + (-4)^2
AC =√16 + 16
AC = √32
AC =4√2
Now let us find another diagonal
By Distance Formula
BD =√(x2-x4)^2 + (y2 - y4 )^2
BD=√(4-(-2) )^2 +(5-(-1) )^2
BD=√(6)^2 + (6)^2
BD=√36+36
BD=√72
BD=√36 ×2
BD=6√2
NOW LET US FIND AREA OF RHOMBUS
AREA=1/2 × PRODUCT OF LENGTH OF DIAGONALS
AREA=1/2 × AC × BD
AREA=1/2 × 4√2 × 6√2
AREA=1/2 × 48
AREA= 24 sq.units
Therefore,Area of rhombus is 24 sq.units