Question

What is the length of the base of a parallelogram that has an area of 120 square inches and a height of 8 inches?

Answer 1

Hint: Assume the base of the parallelogram as b and its height as h. Now, apply the formula for the area of a parallelogram given as $A=b\times h$ where A is the area. Substitute the given values of A = 120 square inches and h = 8 inches and calculate the value of b to get the answer.

Complete step by step solution:
Here we have been provided with the area of a parallelogram as 120 square inches with its height as 8 inches. We are asked to find the length of the base of this parallelogram.

Now, in the above figure we have drawn a parallelogram ABCD with its base as B and height as h. we have joined the diagonal AC to form two triangles. We know that the diagonal of a parallelogram divides it into two congruent triangles and congruent triangles have equal areas. So the area of the parallelogram (A) can be given as: -
$\Rightarrow A=Ar.\left( ABC \right)+Ar.\left( ACD \right)$
Using the formula for the area of a triangle given as $\dfrac{1}{2}\times b\times h$ we get,
$\begin{align}
  & \Rightarrow A=\dfrac{1}{2}\times b\times h+\dfrac{1}{2}\times b\times h \\
 & \Rightarrow A=b\times h \\
\end{align}$
Substituting the given values of A = 120 and h = 8 we get,
$\begin{align}
  & \Rightarrow 120=b\times 8 \\
 & \Rightarrow b=15 \\
\end{align}$
Hence, the length of the base of the parallelogram is 15 inches respectively.

Note: You must remember the properties of a parallelogram to solve the above question. Note that the perpendicular distance between the two parallel lines are always equal. Remember the formula of the area of all the special quadrilaterals like square, rectangle, rhombus, trapezium etc. At last note that the unit of base will be inches because area is in square inches and height is also in inches.