Question

5. The area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
d)32 s
12 sq.unit
b)
24 sq.unit
c) 30 sq.unit
(d) 32 sq unit
​

Answer 1

Answer:

24 sq. units.

hope this helps  you...

Answer 2

$\huge\purple{Required \: Answer :}$

b) 24 sq. unit

$\huge\red{Explanation :}$

Let A(3,0) B(4,5) C(-1,4) and D(-2,-1) are the vertices of the rhombus.

Length of diagonal AC = √(x₂ - x₁)² + (y₂ - y₁)²

• x₁ = 3 y₁ = 0
• x₂ =-1 y₂ = 4

= √(-1 - 3)² + (4 - 0)²

= √(-4)² + (4)²

= √16 + 16

= √32

Length of diagonal BD = √(x₂ - x₁)² + (y₂ - y₁)²

• x₁ = 4 y₁ = 5
• x₂ = -2 y₂ = -1

= √(-2-4)² + (-1-5)²

= √(-6)² + (-6)²

= √36 + 36

= √72

Area of rhombus = (1/2) x √32 x √72

= (1/2)4√2 x 6√2

= 24 square units.

$\huge\sf\implies{Thanks : ❤}$