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In the following figure, find the area of the shaded portion :

 Q. 10.     In the following figure, find the area of the shaded portion:

               

 

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R Riya

Area  of shaded portion = Area of the whole square ( PQRS ) - Area of three triangles ( PTQ , STU and QUR )

Area of the square with side 20cm is

\Rightarrow a^2 = (20)^2 =400 \ cm^2

Area of triangle PTQ with base 10 cm and height 20 cm is

\Rightarrow \frac{1}{2} \times \ base \times height =\frac{1}{2} \times 10 \times 20 = 100 \ cm^2

Area of triangle STU with base 10 cm and height 10 cm is

\Rightarrow \frac{1}{2} \times \ base \times height =\frac{1}{2} \times 10 \times 10 = 50 \ cm^2

Area of triangle QUR with base 20 cm and height 10 cm is

\Rightarrow \frac{1}{2} \times \ base \times height =\frac{1}{2} \times 20 \times 10 = 100 \ cm^2

Now, Area  of the shaded portion is 

\Rightarrow 400 - (100+100+50)

\Rightarrow 400-250=150 \ cm^2

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