Can you help me determine the area enclosed by the graph?

Question

Can you help me determine the area enclosed by the graph?

Currently, I am in the process of creating a graph plotting website for my homework assignment. After successfully drawing the graph using graph.js, I am now faced with the challenge of calculating the area under the graph.

Attached is a screenshot of the graph: https://i.sstatic.net/enmA8.png

My goal is to determine the total grey area underneath the graph.

Below is the code used to generate the graph using graph.js:

new Chart(document.getElementById("line-chart"), {
    type: 'line',
    data: {
    labels: labels,
    datasets: [{
            data : graphValue,
            borderwidth : 1,
            label : lineLabel,
            fill : true,
            lineTension : 0,
            pointBackgroundColor : 'rgba (83,81,84,1)',
            borderColor : 'rgba(83,81,84,1)'
    }]
    },
    options: {
        responsive: false,
        title: {
            display: true,
            text: graphName
      },
        scales : {
            yAxes : [{
                ticks : {
                    beginAtZero : true,
                    min :0,
                    max :200
                }
            }]
        }
    }
    });

The values used for the graph are simply an array of numbers passed from the HTML page:

var graphValue = [98,12,19,64,85,91,56,181,171,90];

javascript chart.js

Answer 1

Answer №1

When analyzing your graph, it is important to note that each segment forms a trapezium with a fixed height of 1 unit. To calculate the total area under the curve, you simply need to iterate through the graphValue array and compute the area of each trapezium.

The formula for calculating the area of a trapezium is:

Area = 0.5 * (a + b) * h where a & b represent the two parallel sides of the trapezium, and h denotes the distance between them.

Here's the code snippet that can help you solve this problem:

var graphValue = [98,12,19,64,85,91,56,181,171,90];
var area = 0; // Initialize area to zero
var height = 1; // Fixed height value between parallel sides
for(var i=1; i<graphValue.length; i++) {
    area += 0.5 * (graphValue[i] + graphValue[i-1]) * height;
    // Where a = graphValue[i], b = graphValue[i-1]
}

console.log(area); // Output: 773 for this given example

Answer 2

When analyzing your graph, it is important to note that each segment forms a trapezium with a fixed height of 1 unit. To calculate the total area under the curve, you simply need to iterate through the graphValue array and compute the area of each trapezium.

The formula for calculating the area of a trapezium is:

Area = 0.5 * (a + b) * h where a & b represent the two parallel sides of the trapezium, and h denotes the distance between them.

Here's the code snippet that can help you solve this problem:

var graphValue = [98,12,19,64,85,91,56,181,171,90];
var area = 0; // Initialize area to zero
var height = 1; // Fixed height value between parallel sides
for(var i=1; i<graphValue.length; i++) {
    area += 0.5 * (graphValue[i] + graphValue[i-1]) * height;
    // Where a = graphValue[i], b = graphValue[i-1]
}

console.log(area); // Output: 773 for this given example

Can you help me determine the area enclosed by the graph?

Answer №1

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