SOLUTION: The figure below is a trapezium in which AB=40 cm, BC=25 cm, CD=12 cm and AD=17 cm. Calculate the area of the trapezium.

Algebra ->  Finance -> SOLUTION: The figure below is a trapezium in which AB=40 cm, BC=25 cm, CD=12 cm and AD=17 cm. Calculate the area of the trapezium.       Log On


   

Question 1199005: The figure below is a trapezium in which AB=40 cm, BC=25 cm, CD=12 cm and AD=17 cm. Calculate the area of the trapezium.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a sketch, showing altitudes DE and CF:



The quick path to the answer is to guess that all the numbers in the problem are whole numbers. So look for Pythagorean triples. With AD=17, it is likely that AE is 8 and the altitude h is 15; and with the altitude 15, FB would be 20. And 8+12+20 = 40, as required.

So the bases are 12 and 40, and the height is 15; the area is 15*((12+40)/2) = 15*26 = 390.

ANSWER: 390

If you want a formal algebraic solution....

AE+=+sqrt%2817%5E2-h%5E2%29
FB+=+sqrt%2825%5E2-h%5E2%29

Then

sqrt%2817%5E2-h%5E2%29%2B12%2Bsqrt%2825%5E2-h%5E2%29=40

I won't go through the whole process of solving that equation....

To solve it, isolate one of the square roots on one side of the equation and square both sides. That will leave you still with one square root; again isolate it and square both sides. Now you will have no square roots left; and the remaining equation can be solved for the altitude h with only mildly ugly arithmetic.