Question

algebraic expression​

Answer 1

$105 \: {cm}^{2}$

Step-by-step explanation:

$the \: \: area \: \: of \: \: shaded \: \: region = \\ Area \: \: of \: \: the \: \: whole \: \: rectangle - Area \: \: of \: \: the \: \: rectangle \: \: formed \: \: at \: \: the \: \: four \: \: corners \\ then, \: \: \: \: \boxed{the \: \: area \: \: of \: \: shaded \: \: region = 18 \times 25 - 4(SP×PD)} \\calculate , \: \: \: \: SP = \frac{25 - 2}{2} = \frac{23}{2} \: cm \: \: \: and \: \: \: PD = \frac{18 - 3}{2} = \frac{15}{2} \: cm \\ Now, \: \: \: \: putting \: \: values \\ the \: \: area \: \: of \: \: shaded \: \: region =18 \times 25 - 4( \frac{23}{2} \times \frac{15}{2} ) \\ = 450 - 4 \times \frac{345}{4} \\ = 450 - 345 \\ = 105 \: {cm}^{2}$