Question

In the given figure,
LMN is a right triangle in which $\angle M={90}^{\circ }$. P and Q are mid-points of LM and LN respectively.
If LM = 9 cm, MN = 12 cm and LN = 15 cm, find :
(i) the perimeter of trapezium MNQP.
(ii) the area of trapezium MNQP.

Answer 1

$LM=9$cm

$MN=12$cm

$LN=15$cm

$\therefore PM=4.5$cm

$QN=7.5$cm

And we know that the line joining the mid points of the two sides of a triangle is parallel to the third side and is equal to half of it.

$\therefore PQ=\frac{1}{2}MN=6$cm

(i)Perimeter of trapezium $MNQP=(4.5+7.5+12+6)$

$=24+6$

$=30$cm

(ii)Area of trapezium$=\frac{1}{2}\times$(sum of parallel sides)$\times$ (height)

$=\frac{1}{2}\times (12+6)\times 4.5=9\times 4.5$

$=40.5$cm