Question

The square above has an area of 100. If Q is the midpoint of AC and I? is the midpoint of BD, what is the area of the shaded area?

• A. 40
• B. 50
• C. 60
• D. 75

Answer 1

The correct option is B 50

Area of square is $100$

$\Rightarrow a^2=100$

$\Rightarrow a=10$

$QC=\left(\frac{1}{2}\right)\times AC=\frac{10}{2}=5$

$BR=\left(\frac{1}{2}\right)\times BD=10/2=5$

$CD=AB=10=AC=BD$

Area of triangle $QCD$ is $=\left(\frac{1}{2}\right)\times QC\times CD=\left(\frac{1}{2}\right)\times 5\times 10=25$

Area of triangle $ABR$ is $=\left(\frac{1}{2}\right)\times AB\times BR=\left(\frac{1}{2}\right)\times 10\times 5=25$

Area of shaded region is area of square $-$ ($2$ area of triangles)

$\Rightarrow 100-(25+25)=50$

Area of shaded region is $=50$