Question

In the figure, ABCD is a rectangle and line MN cuts the rectangle into half. Triangle MNO and triangle MNP are identical triangles. The area of shaded region is ___________

• A. More than 180 $c{m}^2$
• B. Equal to 120 $c{m}^2$
• C. more than 120 $c{m}^2$
• D. Less than 120 $c{m}^2$

Answer 1

Answer: (B)

Equal to 120 $c{m}^2$

In area of triangle MNO =area of triangle MNP=$\frac{1}{2}Hight\times Base$=$\frac{1}{2}5\times 20$=50$c{m}^2$
Area of triangle MNF=triangle MNE=$\frac{1}{2}Hight\times Base$=$\frac{1}{2}8\times 20$=80$c{m}^2$
Then areaof triangle2( MNP+MNO)=$2\times 50\times 2=200c{m}^2$
Or area of triangle(MNF+MNE+MEN+MFN)=$80\times 4=320c{m}^2$
SO area of shaded region = 320-200=120 $c{m}^2$