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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) Use the trapezoidal rule to determine the surface area of the pool.

(ii) The pool has a uniform depth of 120 cm. Determine the volume of water in the pool.

(iii) What is the capacity of the pool (to the nearest 10 litres)?

Answer.(i) SA = 85.6 m2
(ii) Volume = 102.72 m3.
(iii) Capacity = 102,700 litres.
 

3. A shape is shown in the diagram below.

Using two applications of the Trapezoidal Rule, estimate the approximate area of the shape.

Answer. Area = 750 u2.
  4. The shape and dimensions of a park are shown in the diagram below.

(i) Use the Trapezoidal Rule with two applications to estimate the area of the park.

(ii) If it takes an average of 2 minutes to cut 1,250 m2 of the grass, how long will it take to cut all the grass in the park?

Answer.(i) Area = 173,250 m2.
(ii) 4.62 hours = 4 hours 38 mins.
  5. The diagram below shows a swimming pool with a sloping bottom from both ends. The two slopes are NOT equally spaced from the ends.

Using the measurements given:

(i) find the area of each of the two trapezia which make up the front side;

(ii) find the maximum volume of water which the swimming pool could hold.

(iii) Find the capacity of the swimming pool (to the nearest 10 litres).

Answer.(i) AreaLHS = 8 m2
AreaRHS = 13.5 m2.
(ii) Volume is 107.5 m3
(iii) Capacity is 107,500 litres.
Multiple trapezia. 6. The diagram below shows a paddock ADB bounded by a river AB and three parallel fences.

The distances of each fence from the end of the paddock to the river are:

GH = 8 m; CD = 12 m; EF = 10 m.

All distances AG, GC, CE and EB are 5 m.

Use the Trapezoidal Rule to find the approximate area of the paddock.

Answer. Area = 150 m2.
  7. A park fronts on to a lake as shown in the diagram below.

The width of the park (AB) is 75 metres. The distances from the top boundary to the lake are shown.

Calculate the approximate area of the park using three applications of the Trapezoidal Rule.

Answer.Area = 3,300 m2.
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