How to find the area of ​​a trapezium?

How to find the area of ​​a trapezium?

Before looking at the area of ​​the trapezium we need to keep in mind the shape of the trapezium. A trapezium is a figure enclosed between parallel lines. If closed without parallel lines it becomes a quadrilateral.

Parallel lines can be either horizontal or vertical. That is, it is a trapezium whether it is bounded by horizontal parallels or between vertical parallels.

Perhaps sandwiched between horizontal parallels and vertical parallels it becomes parallelogram. That is if the every opposite sides are parallel then it is parallelogram. We have already seen about the area of ​​a parallelogram called bh in square units. Therefore, for a trapezium, only one pair of sides must be parallel, i.e. only one pair of opposite sides must be parallel.

We will ask you to remember the window of the car to easily remember trapezium.

Now let's see how to draw a trapezium.

Draw two parallel lines. Draw the bottom line big and the top line small as shown in the picture. Let us name the line below as AB. Let us name the above line as CD.

Next we close the parallel lines by drawing lines on the sides. Now the enclosed figure is the trapezium. See what you have done so far in the process.

Next let's name the size of the sides. Let us denote the bottom line size AB that is the size of the below side by the variable a. Let's denote the top line CD that is the size of the above side by the variable b.

Next let's draw a perpendicular line from the bottom to the top. This is the height of the trapezium. Let us denote this by the variable h. You can see all this in the above picture.

Now let's draw to extend to the bottom side i.e. side AB as shown in the picture and extend it well. You can see in this picture.

Did you draw? Isn't the BC side next? i.e. the right side. Let us note its central point. Let's name that center as E. You can also see this in the picture.

Now what we are going to do is extend a line from D through E as shown in the figure.

Did you draw? Does the line we just drew and the line we drew earlier extending the bottom intersect at F?

Now see that you get two triangles up and down along the DEF line. Note that the top triangle is colored green and the bottom triangle is orange for your understanding.

All you have to do is cut out the top green triangle and turn it upside down and left and right and glue it to the orange triangle. Does the green triangle fit perfectly into the orange triangle? Check it out in the image below. So point B becomes C and point F becomes D?

What have we done now? Do we cut the part above the trapezium and stick it to the right of the trapezium? Have we rearranged what used to be a trapezium into a triangle without changing size? So the size of the area that was trapezium and the area that is now triangular has not changed? Are the two the same?

If we now find the area of ​​the triangle, is it not the area of ​​the trapezium? I don't think they will have any confusion about this.

Now let's find the area of ​​the triangle?

Area of ​​triangle is ½bh square units?

Isn't the base b of this triangle joined to the base a and the top b of the trapezium? So the base is (a + b) units. Since the height h corresponds to the same triangle as the height of the trapezium, let's take it as h units.

Now the area of ​​the triangle we have created from the trapezium is ½ (a + b)×h square units, right? If we take this as ½ h(a + b) square units then what is the formula for the area of ​​the trapezium? Now you understand.

You know what we want to see next. We will see it tomorrow.

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