Question

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

Answer 1

Point

A = (3,0)

B = (4,5)

C = (-1,4)

D = (-2,-1)

Area of a rhombus = diagonal A + diagonal B / 2

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