Question

ABCD is a rectangle having length 30 cm and breadth 25 cm. P, Q, R and S are the midpoints of line segments AB, BC, CD and AD respectively. What is the area of the shaded part?

• A. $375m^2$
• B. $375c{m}^2$
• C. $475c{m}^2$
• D. $425c{m}^2$

Answer 1

The correct option is B $375c{m}^2$

Given: Length of the rectangle ABCD = AB = SQ = DC = 30 cm
Breadth of the rectangle ABCD = AD = PR = BC = 25 cm
PQRS can be considered as the combination of two triangles i.e. $△PSR$ and $△PQR$
Here, PR is the base of the two triangles.
Area of $\Delta PQR=\frac{1}{2}\times PR\times height$
$=\frac{1}{2}\times 25\times 15$
$=\frac{375}{2}c{m}^2$
Similarly, area of $\Delta PSR=\frac{1}{2}\times PR\times height$
$=\frac{1}{2}\times 25\times 15$
$=\frac{375}{2}c{m}^2$
$\therefore$ Area of shaded region = Area of rectangle - (area of $\Delta PQR$ + area of $\Delta PSR$)
$=(30\times 25)-(\frac{375}{2}+\frac{375}{2})$
$=750-375c{m}^2=375c{m}^2$