Question

A swimming pool, 30 m long has a depth of water of 80 cm at one end and 2.4 m at the other end. Find the area of the vertical cross-section of the pool along the length.

Answer 1

Hint:
A quadrilateral with at least one pair of parallel sides is known as Trapezium.
Here we have found that the swimming pool is in the shape of trapezium so using the formula of area of trapezium we will find the required answer.

Complete step-by-step answer:
It is given that the swimming pool, 30 m long, has a depth of water of 80 cm at one end and 2.4 m at the other end.
The depth of water at one end is \[80{\text{ }}cm = 0.8{\text{ }}m\]
Here we convert cm into m since all the units should be the same.
If we consider the vertical cross section of the swimming pool then we will get a Trapezium.
We need to find out the area of the vertical cross-section of the pool along the length, which is the same as the area of the trapezium.
The area of a trapezium is =\[\dfrac{1}{2}\] × (Sum of the two parallel sides) × height
Here the length parallel sides are 0.8 m and 2.4 m respectively, also the height is given as 30m.
\[ = \dfrac{1}{2}(.8 + 2.4) \times 30\]
Let us solve the above equation to find the value of area
\[ = \dfrac{1}{2} \times 3.2 \times 30 = 48{m^2}\]
Hence, we have found the area of the vertical cross-section of the pool along the length is \[48{m^2}\].

Note:Trapezium: The trapezium is a quadrilateral with two parallel sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.