Question

Find the missing values.\[\]

Answer 1

Hint: We know that area of the parallelogram is the product of the lengths of base and height. If the height of the parallelogram is $h$ and base is $b$ the area $A$ is given by $A=bh$.We put the known values given in the question for each rows corresponding to serial numbers a, b, c, d, and find the respective known. \[\]

Complete step by step answer:
We know that a parallelogram is a quadrilateral where the opposite sides are equal in length and parallel to each other. We have drawn the figure of the parallelogram ABCD where AB=CD and AD=BC. The parallelogram also has equal opposite angles. If draw any perpendicular from any vertex on the opposite side, the perpendicular is called the height of the parallelogram conventionally denoted as $h$ and the where the opposite side is called base denoted as $b.$ In the figure the perpendicular is drawn from vertex D on AB. So $h=DF,b=AB$. \[\]

We also know that area of the parallelogram is the product of the lengths of base and height. So the area $A$ of the parallelogram can be written as
\[A=AB\times DF= h\times b\]

Now let us observe the given table.\[\]

(a) We see that for serial number ‘a’ in the first row the base $b$ and area $A$ of the parallelogram is given. The height is missing values. Here we have $b=20\text{cm},A=246\text{c}{{\text{m}}^{2}}$. We put these value in the formula for area and get the height $h$ in cm.
\[\begin{align}
  & A=h\times b \\
 & \Rightarrow 246=h\times 20 \\
 & \Rightarrow h=\dfrac{246}{20}=12.3 \\
\end{align}\]
(b) We see that for serial number ‘b’ in the second row the height ‘h’ and area $A$ of the parallelogram is given. The base is the missing value. Here we have $h=15\text{cm},A=154.5\text{c}{{\text{m}}^{2}}$. We put these value in the formula for area and get the base $b$ in cm.
\[\begin{align}
  & A=h\times b \\
 & \Rightarrow 154.5=15\times b \\
 & \Rightarrow b=\dfrac{154.5}{15}=10.3 \\
\end{align}\]



(c) We see that for serial number ‘c’ in the third row the height ‘h’ and area $A$ of the parallelogram is given. The base is the missing value. Here we have $h=8.4\text{cm},A=48.72\text{c}{{\text{m}}^{2}}$ . We put this value in the formula for area and get the base $b$ in cm.
\[\begin{align}
  & A=h\times b \\
 & \Rightarrow 48.72=8.4\times b \\
 & \Rightarrow b=\dfrac{48.72}{8.4}=5.8 \\
\end{align}\]
(d) We see that for serial number ‘a’ in the first row the base $b$ and area $A$ of the parallelogram is given. The height is missing values. Here we have $b=15.6\text{cm},A=16.38\text{c}{{\text{m}}^{2}}$ . We put these value in the formula for area and get the height $h$ in cm.
\[\begin{align}
  & A=h\times b \\
 & \Rightarrow 16.38=h\times 15.6 \\
 & \Rightarrow h=\dfrac{16.38}{15.6}=1.05 \\
\end{align}\]
We now fill the table with the obtained value.\[\]

Note:
We only need to be careful of the division in decimals If the angles of the parallelogram is right angles, then it is called a rectangle whose area is $A=ab$ where $a,b$ are lengths of the sides of the rectangle. If all sides of the rectangle are equal the rectangle is square whose area is ${{a}^{2}}$ where $a$ length of the side.