Question

find area of rhombus​

Answer 1

area of rhombus= diagonal 1× diagonal 2

=12×5

=60 sq unit

Answer 2

Answer:

Area of Rhombus Using Diagonals: Method 1

Consider a rhombus ABCD, having two diagonals, i.e. AC & BD.

Step 1: Find the length of diagonal 1, i.e. d1. It is the distance between A and C. The diagonals of a rhombus are perpendicular to each other making 4 right triangles when they intersect each other at the center of the rhombus.

Step 2: Find the length of diagonal 2, i.e. d2 which is the distance between B and D.

Step 3: Multiply both the diagonals, d1 and d2.

Step 4: Divide the result by 2.

The resultant will give the area of a rhombus ABCD.

Let us understand more through an example.

Example 1: Calculate the area of a rhombus having diagonals equal to 6 cm and 8 cm.

Solution:

Given that,

Diagonal 1, d1 = 6 cm

Diagonal 2, d2 = 8 cm

Area of a rhombus, A = (d1 × d2) / 2

= (6 × 8) / 2

= 48 / 2

= 24 cm2

Hence, Area of a rhombus is 24 cm2.

Area of Rhombus Using Base and Height: Method 2

Step 1: Find the base and the height of the rhombus. The base of the rhombus is one of its sides, and the height is the altitude which is the perpendicular distance from the chosen base to the opposite side.

Step 2: Multiply the base and calculated height.

Let us see understand this through an example:

Example 2: Calculate the area of a rhombus if its base is 10 cm and height is 7 cm.

Solution:

Given,

Base, b = 10 cm

Height, h = 7 cm

Area, A = b × h

= 10 × 7 cm2

A= 70 cm2

Area of Rhombus Using Trigonometry: Method 3

Step 1: Square the length of any of the sides.

Step 2: Multiply it by Sine of one of the angles.

Let us see one example.

Example 3 Calculate area of a rhombus if the length of its side is 2 cm and one of its angle A is 30 degrees.

Solution:

Given,

Side a = 2 cm

Angle A = 30 degrees

square of side a = 2 × 2= 4 cm2

Area, A= s2 × sin (30)

A= 4 × 1/2

A= 2 cm2

Practice Question Based on Area of Rhombus Formula

Question 1: Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Solution:



Area of Rhombus Example Question

ABCD is a rhombus in which AB = BC = CD = DA = 17 cm

Diagonal AC = 16 cm (with O being the diagonal intersection point)

Therefore, AO = 8 cm

In ∆ AOD,

AD2 = AO2 + OD2

⇒ 172 = 82 + OD2

⇒ 289 = 64 + OD2

⇒ 225 = OD2

⇒ OD = 15

Therefore, BD = 2 × OD

= 2 × 15

= 30 cm

Now, area of rhombus

= ½ × d1 × d2

= ½ × 16 × 30

= 240 cm2