Question

From a thin metallic piece, in the shape of a trapezium $ABCD$, in which $AB\parallel CD$ and $\angle BCD={90}^{\circ }$, a quarter circle $BEFC$ is removed (see figure). Given $AB=BC=3.5cm$ and $DE=2cm$, calculate the area of the remaining piece of the metal sheet.

Answer 1

Area of shaded region=ar. trap-ar. sector

$=\frac{1}{2}(AB+CD)\times BC-\frac{1}{4}\times \pi r^2$

$=\frac{1}{2}(3.5+5.5)\times 3.5-\frac{1}{4}\times \frac{22}{7}\times {\left(3.5\right)}^2$

$=15.75-9.625=6.125c{m}^2$