Question

In the figure. $X$ and $Y$ are the mid-points of $AB$ and $AC$ respectively. Given that $BC=6$ cm. $AB=5\cdot 4$ cm and $AC=5\cdot 0$ cm. Calculate the perimeter of trapezium $YXBC$.

• A. $14\cdot 2$ cm
• B. $15\cdot 4$ cm
• C. $16\cdot 8$ cm
• D. none of the above

Answer 1

The correct option is A $14\cdot 2$ cm

Given, X and Y are the mid points of AB and AC. hence, by mid point theorem,
$XY=\frac{1}{2}BC$
$XY=\frac{1}{2}\left(6\right)$
$XY=3$ cm
Perimeter of trapezium XYBC = $XY+YC+BC+XB$
Perimeter of trapezium XYBC = $XY+\frac{1}{2}AC+BC+\frac{1}{2}AB$
Perimeter of trapezium XYBC = $3+\frac{1}{2}\left(5\right)+6+\frac{1}{2}\left(5.4\right)$
Perimeter of trapezium XYBC = $14.2$ cm