Question

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

[Hint: Area of a rhombus = 1/2 (product of its diagonals)]

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Answer 1

Answer:

Explanation:

Given :

• Vertices are, (3, 0), (4, 5), (-1, 4) and (-2,- 1).

To Find :

• The area of a rhombus.

Solution :

Let, R(3, 0), O(4, 5), S(-1, 4) and E(-2,-1).

We need to find RS & OE,

• Finding RS ::

Apply distance formula,

RS = √(-1 - 3)² + (4 - 0)²

=> RS = √(-4)² + 4²

=> RS = √16 + 16

=> RS = √32

=> RS = 4√2 units

• Finding OE ::

Apply distance formula,

OE = √(-2 - 4)² + (-1 - 5)²

=> OE = √(-6)² + (-6)²

=> OE = √36 + 36

=> OE = √72

=> OE = 6√2 units

Now,

• Area of a rhombus = ¹/2 × RS × OE

=> Area = ¹/2 × 4√2 × 6√2

=> Area = 2√2 × 6√2

=> Area = 2 × 6 × √2 × 2

=> Area = 12 × 2

=> Area = 24 sq. units

Hence :

The area of a rhombus is 24 sq. units.

Answer 2

Answer:

Answer

REF.Image

Let the points are A(3,0), B(4,5), C(-1,4) and D(-2,-1)

BD=

(−2−4)

2

+(−1−5)

2

=

(−6)

2

+(−6)

2

=

36+36

=

72

=6

2

units

AC=

(−1−3)

2

+(4−0)

2

=

(−4)

2

+(4)

2

=

16+16

=

32

Now, area of rhombus ABCD

=

2

1

× (Product of diagonals)

⇒ Area of rhombus =

2

1

×(AC×BD)

=[

2

1

×4

2

×6

2

] sq. units

=(2

2

×6

2

) sq. units = 24 sq. units.

please refer to that pic instead of this