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

Answer

Verified

364.2k+ views

Hint: In this question, first draw the diagram and mark the length of side, altitude and diagonal it will give us a clear picture then use the formula of area of rhombus.

Complete step-by-step answer:

From figure,

Side of Rhombus PQRS, PQ=6cm

Altitude from point S to the side PQ, ST=4cm

We know rhombus is a parallelogram so the area of parallelogram is product of base and altitude.

Now, Area of rhombus \[ = {\text{Base}} \times {\text{height}}\]

$

\Rightarrow PQ \times ST \\

\Rightarrow 6 \times 4 \\

\Rightarrow 24c{m^2} \\

$

So, the area of a rhombus is 24cm

Now, in the question given length of one diagonal, $PR = {d_1} = 8cm$ .

To find the length of another diagonal we use the area of the rhombus.

Area of rhombus $ = \dfrac{{{\text{product of diagonals}}}}{2} = \dfrac{{{d_1} \times {d_2}}}{2}$

We already calculate the area of the rhombus so put the value of area in the above formula.

$

\Rightarrow 24 = \dfrac{{{d_1} \times {d_2}}}{2} \\

\Rightarrow 48 = 8 \times {d_2} \\

\Rightarrow {d_2} = 6cm \\

$

The length of the other diagonal, $SQ = {d_2} = 6cm$ .

So, the area of the rhombus is 24cm

Note: Whenever we face such types of problems we use some important points. We use the area of rhombus in two different ways. If we need area we use area of parallelogram but if we need diagonals so we use that formula of area in which diagonals present.

Complete step-by-step answer:

From figure,

Side of Rhombus PQRS, PQ=6cm

Altitude from point S to the side PQ, ST=4cm

We know rhombus is a parallelogram so the area of parallelogram is product of base and altitude.

Now, Area of rhombus \[ = {\text{Base}} \times {\text{height}}\]

$

\Rightarrow PQ \times ST \\

\Rightarrow 6 \times 4 \\

\Rightarrow 24c{m^2} \\

$

So, the area of a rhombus is 24cm

^{2}Now, in the question given length of one diagonal, $PR = {d_1} = 8cm$ .

To find the length of another diagonal we use the area of the rhombus.

Area of rhombus $ = \dfrac{{{\text{product of diagonals}}}}{2} = \dfrac{{{d_1} \times {d_2}}}{2}$

We already calculate the area of the rhombus so put the value of area in the above formula.

$

\Rightarrow 24 = \dfrac{{{d_1} \times {d_2}}}{2} \\

\Rightarrow 48 = 8 \times {d_2} \\

\Rightarrow {d_2} = 6cm \\

$

The length of the other diagonal, $SQ = {d_2} = 6cm$ .

So, the area of the rhombus is 24cm

^{2}and the length of the other diagonal is 6cm.Note: Whenever we face such types of problems we use some important points. We use the area of rhombus in two different ways. If we need area we use area of parallelogram but if we need diagonals so we use that formula of area in which diagonals present.

Last updated date: 29th Sep 2023

â€¢

Total views: 364.2k

â€¢

Views today: 5.64k

Recently Updated Pages

What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Who had given the title of Mahatma to Gandhi Ji A Bal class 10 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

How many millions make a billion class 6 maths CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE