Leaving Cert Mathematics Area & Volume: The diagram below shows a shape

Question

The diagram below shows a shape with two straight edges and one irregular edge. By dividing the edge [AB] into five equal intervals, use the trapezoidal rule to estimate the area of the shape.

Record your constructions and measurements on the diagram. Give your answer correct to the nearest cm²:

The line AB is approximately 16.4cm, so each interval will be 16.4/5 = 3.28 cm long. We then measure the height of the shape at each of these points:

Note that the height of the graph at the endpoint B is 0. From the Formula and Tables book, the Trapezoidal Rule gives the approximate area as:

$$
Area = \frac{h}{2} [y_1 + 2(y_2 + y_3 + \ldots + y_n)]
$$

where $h$ is the width of the subintervals. Thus, the area of our shape is given by:

Area = 3.28[ (4.9 + 0 + 2(6.3 + 5.5 + 3.75 + 4.15)) ]

which is equal to 73 cm² correct to the nearest cm².

The diagram below shows a shape with two straight edges and one irregular edge - Leaving Cert Mathematics - Question 5 - 2011

Worked Solution & Example Answer:The diagram below shows a shape with two straight edges and one irregular edge - Leaving Cert Mathematics - Question 5 - 2011

Calculate the Length of Each Interval

Measure the Heights at Each Interval

Apply the Trapezoidal Rule

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