Answer
Verified
480.3k+ 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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE