Question

the quadrilateral with the vertices A(0,0),B(5,0),C(8,4)& D(3,4) IS A RHOMBUS.find it's area and perimeter

Answer 1

its perimeter is 20 units
because by distance formula 
√(3-0)² + (4-0)²
gives
√25 which is 5units 
since all the sides are equal there for its perimeter is 4 ×5 = 20 units

AREA=length of one diagonal × length of other diagonal × 1/2
therefore,
by distance formula
√(8-0)² + (4-0)²=√64 +16 =√80units =length of one diagonal
√(5-3)² + (0-4)²= √4 + 16 =√20 units = lenght of the second diagonal
area = √80 × √20 × 1/2
       = 4√5 × 2√5 ×1/2
       = 20 unit²
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