Question

Find the formulas for the area of parallelogram and triangle by using the formula of the area of trapezoid.

Answer 1

Hint: A trapezoid is a two dimensional shape, also known as trapezium. It has four sides, two are parallel and two are non-parallel, and the parallel sides are called the base of the trapezium and non-parallel sides are called the legs of the trapezium.

Formula used: Area of trapezium$ = \dfrac{1}{2} \times (a + b) \times h$
Where, a and b are two parallel sides of the trapezium and h is the distance between the two parallel sides.

Complete step by step solution:
In this problem, we have to find the formulas of area of parallelogram and triangle by using the formula of the area of trapezium. Area of trapezium can become the area of parallelogram if both the opposite sides of the trapezoid are equal and parallel to each other. So, to make a parallelogram, we have to consider both the sides of the trapezium equal, which means,
$a = b$
Now, we will substitute it in the above formula of area of trapezium.
$
   \Rightarrow \dfrac{1}{2} \times (a + a) \times h \\
   \Rightarrow \dfrac{1}{2} \times (2a) \times h \\
 $
On further solving, we get,
$ \Rightarrow a \times h$
Which means the product of base and height, is the area of parallelogram.
Now, area of trapezium can become the area of triangle if, one of the sides of parallelogram is of zero length, means,
$a = 0$
Now, we will substitute it in the above formula of area of trapezium.
$ \Rightarrow \dfrac{1}{2} \times (0 + b) \times h$
On further solving, we get,
$ \Rightarrow \dfrac{1}{2} \times b \times h$
Which means, the half of the product of the base and height, is the area of the triangle.

Note: To solve this problem, we must have known about the properties of parallelogram and the properties of a triangle. As the parallelogram has $4$ sides and opposite sides are parallel to each other and in a triangle there are only $3$sides. If we know about the area of parallelogram and area of triangle, then we can also check whether our answer is correct or not.