Question

The shape of the top surface of the table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

Answer 1

Hint:
To calculate the upper surface area of a table which is a trapezium, we need the sum of parallel sides of a trapezium and the distance between the two parallel sides which is the perpendicular distance given in the question.

Complete step by step solution:
Here we have to find the area of only the upper surface which has a trapezium shape.
Let’s draw only the upper surface of a table and name the trapezium as ABCD.

According to the question:-
\[AB = 1m\]
\[CD = 1.2m\]
\[AP = \] perpendicular distance between AB and CD\[ = 0.8m\]
Now we will use the formula to find the area of trapezium.
We know that Area of trapezium = \[\dfrac{1}{2} \times \] (sum of parallel sides of a trapezium)\[ \times \]Distance between them.
Now,
Area of trapezium \[ = \dfrac{1}{2} \times (AB + CD) \times {\rm{ }}AP\]
Substituting the values of sides in the above equation, we get
\[ \Rightarrow \]Area of trapezium \[ = \dfrac{1}{2} \times (1 + 1.2) \times 0.8\]
Adding the terms inside the bracket, we get
\[ \Rightarrow \]Area of trapezium \[ = \dfrac{1}{2} \times 2.2 \times 0.8\]
Multiplying the terms, we get
\[ \Rightarrow \]Area of trapezium \[ = 0.88{m^2}\]

$\therefore $ Area of trapezium i.e. the area of the upper surface of a table is \[0.88{\rm{ }}{m^2}\].

Note:
Trapezium is also known as trapezoid. The parallel sides of a trapezium are called bases and the other pair of opposite sides which are non parallel are called legs. The distance between the two bases of a trapezium is called height.
Here, we can make mistakes by using the formula of volume instead of are. Area is always found out for a two dimensional surface, whereas volume is found out for a three dimensional surface.