Question

in trapezium, the length of its parallel sides are a and b. the lenght of the lline joining the midpoint of its non parallel sides?

Answer 1

➡️Answer:

length of the line joining the midpoint of its non parallel sides is $EF = \frac{a + b}{2}$

➡️Solution:

Figure shows the given trapezium,length of parallel sides are 'a' and 'b' respectively

Area of Trapezium ABCD=
$\frac{1}{2} (sum \: of \: parallel \: sides) \times perpendicular \: distance \: \\ \\ = \frac{1}{2} (a + b)h$
Let the points E and F are the midpoints of AD and BC respectively.

EF divides the trapezium into two trapezium
ABFE,and EFCD

Area of ABFE + Area of EFCD = Area of ABCD

Area of ABFE$= \frac{1}{2} (EF + b) \frac{h}{2}$

Area of EFCD$= \frac{1}{2} (EF + a) \frac{h}{2}$

So,

$\frac{1}{2} (EF + b) \frac{h}{2} + \frac{1}{2} (EF + a) \frac{h}{2} = \frac{1}{2} (a + b)h\\ \\ EF + b + EF + a = 2(a + b) \\ \\ 2EF = 2a + 2b - a - b \\ \\ 2EF = a + b \\ \\ EF = \frac{a + b}{2}$

so,length of the line joining the midpoint of its non parallel sides is (a+b)/2

Hope it helps you.