Answer
Verified
486k+ 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
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Derive an expression for drift velocity of free electrons class 12 physics CBSE
Which are the Top 10 Largest Countries of the World?
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
The energy of a charged conductor is given by the expression class 12 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Derive an expression for electric field intensity due class 12 physics CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Derive an expression for electric potential at point class 12 physics CBSE