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Find the area of the shaded portion in the following figure:

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160 {cm}^{2}

110 {cm}^{2}

150 {cm}^{2}

130 {cm}^{2}

answer is C.

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Detailed Solution

Consider the figure we have triangle

SR = 10 + 10 = 20 cm

QR = 20 cm

TS = 10 cm

So,

PT = 10 cm

PQ = 20 cm

We seen that in the figure the PQRS is a square
So, the area of square PQRS I

\times

b (l = length, b = breadth)

= 20 \times 20

= 400 {cm}^{2}

Now calculation of the all triangle in the figure by using this formula

\frac{1}{2} \times l \times b

Area of triangle QRU

= 1 / 2 \times 10 \times 20

= 100 {cm}^{2}

Area of triangle

TSU

= 1 / 2 \times 10 \times 10

= 50 {cm}^{2}

Area of triangle QPT

= 1 / 2 \times 10 \times 20

= 100 {cm}^{2}

Finally, we calculated the area of shaded region in the figure
Area of shaded region = Area of square - (Area of triangle QRU + Area of triangle TSU + Area of triangle QPT)
We substitute the value in the concept we obtain

= 400 - (100 + 50 + 100)

= 400 - 250

= 150 {cm}^{2}

Hence area of shaded portion

= 150 {cm}^{2}

Correct option is 3.

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