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.
Last updated date: 25th Mar 2023
•
Total views: 307.5k
•
Views today: 5.84k
Answer
307.5k+ 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 24cm2
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 24cm2 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.
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 24cm2
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 24cm2 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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
