Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

The Trapezoidal Rule - Standard applications.
Test Yourself 1.


 

Two trapezia. 1.
  2.The view of a fancy swimming pool from above is shown in the diagram below together with relevant measurements.

(i)

(ii) BEWARE: 120 cm = 1.2 m.
∴ Volume = 85.6 × 1.2 = 102.72 m3.

(iii) Capacity of the pool = 102,720 L.
 

8.

 

9.

(i)

(ii)

Multiple trapezia. 10.

Step 1: draw up a table to show all the measurements:

Horizontal points: A G C E B
Horizontal measurements: 0 5 10 15 20
Vertical measurements: 0 8 12 10 0

Step 2: Consider each trapezium (even the triangles) and write down the values according to the rule:

Area = distance between the parallel sides:
Divided by 2
Multiplied by the sum of the parallel sides.

Do this for each component:

Step 3: Sum the four areas: A = 20 + 50 + 55 + 25 = 150 m2.
  11. (i) (ii)

Max volume = (8 + 13.5) × 5

= 107.5 m2

 

(iii) Capacity = 107.5 × 1000

= 107,500 litres.

 

12.

Horizontal distance 0 25 50 75
Vertical distance 60 42 30 60

Can calculate the area of each trapezium separately:

OR

Calculate the total area in one go by adding the consecutive pairs of distances in the second line:
  13.
  14.