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) h
#please help me i got stuck i don't know the reason for it and the homework should be submitted #
I can help you understand why the area of the trapezium differs when someone considers the areas of the two right-angled triangles separately and adds them, compared to using the formula for finding the area of a trapezium.
First, let's understand the formula for finding the area of a trapezium. The formula is 1/2(a + b) * h, where 'a' and 'b' are the lengths of the parallel sides of the trapezium, and 'h' is the height (the perpendicular distance between the parallel sides).
Now, let's consider a trapezium that has two right-angled triangles. If we divide the trapezium into two right-angled triangles, we can calculate the area of each triangle separately using the formula for the area of a triangle, which is 1/2 * base * height for right-angled triangles.
Let's say 'A1' represents the area of the first right-angled triangle, and 'A2' represents the area of the second right-angled triangle. To find the total area of the trapezium, one might add A1 and A2 together.
However, there's an important factor to consider. When we add the areas of the two right-angled triangles, we are counting the shared base between the triangles twice. The shared base is the side of the trapezium that is common to both triangles.
On the other hand, when using the formula for finding the area of a trapezium, the shared base is only counted once because it is part of the formula (1/2(a + b) * h). The formula already considers the shared base and incorporates it appropriately, so there is no need to add it separately.
Due to this difference in calculation, if someone adds the areas of the two right-angled triangles separately, it will result in an overestimation of the total area of the trapezium. The formula for finding the area of a trapezium correctly incorporates the shared base and provides an accurate result.
To avoid this discrepancy, it is essential to use the formula for the area of a trapezium (1/2(a + b) * h) rather than adding the areas of the individual triangles when calculating the total area of the trapezium.