Question

$ABCD$ is a rectangle having length $30cm$ and breadth $25cm,P,Q,R,S$ are midpoints of $AB,BC,CD$ and $AD$ respectively. Find the area of the shaded region of the figure.

• A. $375c{m}^2$
• B. $370c{m}^2$
• C. $475c{m}^2$
• D. $450c{m}^2$

Answer 1

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

Area of shaded region $=$ Area of rectangle $-$ Area of all $4$ triangles

A${}_1=$ Area of rectangle $=30\times 25=750c{m}^2$

A${}_2=$ Area of triangle $△SDR=93.75c{m}^2$

A${}_3=$ Area of triangle $△RCQ=93.75c{m}^2$

A${}_4=$ Area of triangle $△QBP=93.75c{m}^2$

A${}_5=$ Area of triangle $△PAS=93.75c{m}^2$

Area of shaded region $=750-4\times 93.75=375c{m}^2$