If a trapezium was drawn such that it has got two right angled triangles,why the area of that trapezium will differ if someone is considering the areas of two right angled triangles lastly he/she add to obtain the total areas from the one who will use the formula for finding trapezium that is 1/2(a+b)
#please help me i got stuck i don't know the reason for it and the homework should be submitted #
man, I can't even figure out the question...
may you direct me how to bring the figure here
I can help you understand why the area of a trapezium calculated using the formula 1/2(a+b) is different from the sum of the areas of two right-angled triangles.
Let's start by understanding the formula for calculating the area of a trapezium. The formula you mentioned, 1/2(a+b), represents the average of the lengths of the parallel sides (a and b) multiplied by the height. This is based on the concept that the area of a trapezium can be represented as the average of the lengths of the parallel sides multiplied by the height.
Now, when we consider two right-angled triangles within the trapezium, we need to understand that these triangles also have a base and a height. To calculate the area of each triangle, we use the formula 1/2(base * height). The sum of the areas of these two triangles would be the area contributed by them within the trapezium.
However, it is important to note that the area of a trapezium calculated using the formula 1/2(a+b) includes the areas of these right-angled triangles as well. This is because the formula accounts for the height of the trapezium and the lengths of both parallel sides, which already consider the contributions from the triangles. Therefore, if we separately calculate the areas of the triangles and add them to the formula for the trapezium, we end up double-counting the areas of the triangles. This results in an erroneous total area for the trapezium.
To avoid double-counting, it is important to either use the formula 1/2(a+b) alone to calculate the area of the trapezium or calculate the areas of the triangles and subtract them from the total area of the trapezium calculated using the formula.