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Hello.

My name is Mr. Clasper and today we are going to be learning how to find the area under a straight line graph.

How can we find the area under a straight line between two specific points? In this case, we've been asked to find the area between where t is equal to one and where t is equal to four.

Well, to do this, if we find t is equal to one and t is equal to four on our graph, this means we're looking for this area.

This is a trapezium.

And to find the area of a trapezium, we could use this formula, where h represents the perpendicular height and a and b are the lengths of my two parallel sides.

Well, looking at the diagram, we can see that we have a perpendicular height of three, and our sides of a and b, our parallel sides are seven and 16 units.

So if we substitute this information into the given formula, we would get a value of 34.

5 units squared.

Let's have a look at speed-time graph.

So we have a similar diagram.

If we think about this carefully, we have our formula to find the area of trapezium and in this case, our perpendicular height is a measure of time and our parallel sides, a and b are both measures of speed.

So we could substitute our information in, and this would give us the area must be equal to half multiplied by the time, multiplied by the speed.

And if we ignore the constant of one half, this leaves time multiplied by speed.

And when we multiply time by speed, we find out a distance they fall on a speed time graph.

If we find the area underneath the graph, the area is equal to the distance.

Here's a question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here is your solution.

So if you draw a trapezium, which has a perpendicular height of four, which is the difference between five and one and the height, sorry, I'll do it again.

So slide four.

And here is your solution.

So if you draw a trapezium, you should find that it has a perpendicular height of four units, which is the difference between five and one, and the two parallel sides we'll have lengths of three and 23.

And then once you have this information, if you put it into the formula to find the area of a trapezium, you should find an area of 52 units squared.

Here's another question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here is the solution.

So once again on the graph, all we need to do is to calculate the area underneath the, sorry, slide five.

And here is your solution.

So all we need to do is to calculate the area underneath the graph.

So in this case, we already have a trapezium.

So if we use the values that we have, find the length of our parallel sides and our perpendicular height, we can calculate that the answer must be 450 metres.

So remember on a velocity-time graph, the area underneath the graph, represents our distance.

Before we try our last problem, let's take a look at this example.

We've been given a trapezium and we know that the area is 26 units squared, however, we don't know one of the parallel sides.

So we have our formula, which is half multiplied by the perpendicular height multiplied by a plus b.

If I substitute all the information that I know, this means that 26, my area, must be equal to half multiplied by four, which is my perpendicular height multiplied by X plus five.

And if I multiply one half by four, this means that this is equal to two lots of X plus five.

If I expand my bracket, this means that 26 is equal to two X plus 10, subtracting 10 from both sides means that 16 must be equal to two X and then dividing both sides by two, means that the length of X must be eight.

Here's your last question.

Pause the video to complete your task and click resume once you're finished.

And here is your solution.

So remember if we're using the formula for the area of a trapezium, looking at the question, we're told that the total distance travelled is 1.

3 kilometres.

This is equivalent to 1,300 metres, and it means that we can make our area of the trapezium equal to 1,300.

From there, if we rearrange the equation, you should find that the correct answer was 40 metres per second.

And that brings us to the end of the lesson.

So in today's lesson, you found out how to find the area underneath the straight line graph.

Have got the exit quiz to show off your brand new skills.

I'll hopefully see you soon.