Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its
diagonals is 8 cm long, find the length of the other diagonal.​

Answer 1

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GIVEN:-

Side = 6 cm.

Altitude = 4 cm.

Diagonal A = 8 cm.

Length of Diagonal B = ?

Area of the rhombus = 6 cm × 4 cm = 24cm2

Let the length of the other diagonal be B.

We know that,

Area of a rhombus = Half of the product of diagonals of the rhombus.

⇒ (1/2) × 8 cm × B = 24cm²

⇒B = (24 × 4) cm = 6 cm.

Therefore, length of the other diagonal B = 6 cm.

WHAT IS A RHOMBUS?

• ◇ Rhombus is a quadrilateral as well as a parallelogram.
• ◇ Rhombus is also known as Rhomb.
• ◇ All sides are equal in length.
• ◇ Diagonals bisect each other at right angle.
• ◇ The opposite sides are parallel.
• ◇ Opposite angles are equal.
• ◇ It is often called a diamond.
• ◇ It is also referred to as convex quadrilateral.

Answer 2

Answer:

Area of rhombus = 24 cm²

Length of the other diagonal = 6 cm.

Step-by-step explanation:

Hi,

Given the side of the rhombus, b = 6 cm

Also, Given the altitude of rhombus , h = 4 cm,

Area of the rhombus when base(side) and altitude(h)

are given is given by A = base * height

Thus, Area of rhombus = 6 * 4 cm²

Area of rhombus = 24 cm².

Given one of the diagonal is of length 8 cm,

Let d₁ = 8 cm.

Let the length of the other diagonal be d₂.

If d₁, d₂ length of the diagonals are known, then

Area of rhombus is given by A = 1/2*d₁*d₂,

But we know, A = 24

Hence, 1/2*d₁*d₂ = 24

1/2*8*d₂ = 24

d₂ = 6 cm.

Hence, length of the other diagonal of rhombus

is 6 cm.

Hope, it helps !