Question

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by these points (in ${cm}^2$).

Answer 1

Apply Pythagoras theorem to find the perpendicular distance of the two lines.

In $\Delta$OEB

${OE}^2$ + ${BE}^2$ = ${OB}^2$

${OE}^2$ = 25 - 9 (perpendicular drawn from Centre to a chord bisects the chord therefore BE = 3cm)

OE = 4cm

Similarly In $\Delta$OFD

${OF}^2$ + ${FD}^2$ = ${OD}^2$

${OF}^2$ = 25 - 16

$\Rightarrow$ OF = 3cm

Area of trapezium

= $\frac{1}{2}$(perpendicular distance between two parallel sides)(sum of the length of the parallel sides)

= $\frac{1}{2}$(4+3)(8+6)

= 49 ${cm}^2$