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

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 !

Answer 2

Since,a rhombus is also a kind of a parallelogram.

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =6×4=24

Since, Area of rhombus is 24 cm².

Also,formula for area of rhombus =$\frac{1}{2}×d_1d_2$

Given,Length of one diagonal =$d_1$=8

Let length of other diagonal =$d_2$

After substituting the values, we get

$24=\frac{1}{2}×8×d_2$

$24=4×d_2$

$4×d_2=24$

$d_2=\frac{24}{4}$

$d_2=6$

Hence, length of other diagonal is 6 cm.