2.4
Chat with our AI personalities
Ah, what a happy little question! To find the area of a rectangle, you simply multiply the length by the width. So, for a 60 by 10 meter rectangle, the area would be 600 square meters. Just imagine all the beautiful landscapes you could create in that much space!
Without knowing where a, b and h are, we have no way of knowing whether ab and ah are lengths, widths or diagonals and consequently, no way of determining the area.
rectangle, quadrilateral, and parallelagram
Half the sum of the parallel sides, times the height between them, that is how you calculate the area of a trapezium.And that is what we learnt at school (to the tune of pop goes the weasel.)______________Here's some more detail, for those who want it:For a trapezoid where h is the height (ie: the distance between the two parallel sides), and a & b are the lengths of the two parallel sides:Area = h (a + b) / 2Proof:If you look at a trapezoid sitting on the longer of its two parallel sides, you will see that it's actually a rectangle in the middle, with a right-angled triangle on each side.The area of the rectangle would be:h x a (where a is the shorter parallel side)For the two right-angled triangles, if c and d are the lengths of the perpendicular sides, then the areas are:(h * c) / 2 and(h * d) / 2So, we add the two triangle areas together, and cancel:(h * c + h * d) / 2= h (c + d) / 2This can be substituted for the following, since in a trapezoid a + c + d = b, hence c + d = b - ah (b - a) /2So, the total area of the trapezoid is the sum of the two formulas:h (b - a) / 2 + h * a(multiply the "h * a" part by 2, and divide be 2 as well, to get a common denominator):= h (b - a) / 2 + 2ha / 2= h (b - a + 2a) / 2= h (b + a) / 2So, there's your proof. A little complicated, but hopefully you get the idea.
I don't know how to sum geometrical figures. I suppose you could count it: one! One trapezoid! Ah ah ah ah ah. The sum of the interior angles of any convex four-sided polygon is 360 degrees. The some of the exterior angles of any convex polygon (no matter how many sides it has) is 360 degrees.