The area of the shaded portion of the figure in $c m^{2}$ is:

1

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5

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6

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2

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Solution

The correct options are
A $1$
B $5$
$W e n a m e t h e g i v e n f i g u r e a s s h o w n . I n t h e g i v e n f i g u r e Δ A B C & Δ D E B a r e r i g h t t r i a n g l e s . A C = 2 c m, B E = 2 c m & C E = 4 c m . ∴ B C = B E + C E = (4 + 2) c m = 6 c m . S o a r Δ A B C = \frac{1}{2} \times B C \times A C = \frac{1}{2} \times 6 \times 2 {c m}^{2} = 6 {c m}^{2} . S i m i l a r l y Δ D E B = \frac{1}{2} \times B E \times D E = \frac{1}{2} \times 2 \times 1 {c m}^{2} = 1 {c m}^{2} . ∴ a r . s h a d e d p o r t i o n A C E D = a r Δ A B C - a r Δ D E B . = (6 - 1) {c m}^{2} = 5 {c m}^{2} . A n s - a r . s h a d e d p o r t i o n A C E D i s 5 {c m}^{2} .$

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