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Area of Trapezium by Division into Shapes of Known Area

DEFG is a squ...

Question

$D E F G$ is a square and $A B C D$ is a rectangle. A straight line is drawn from $A$ passes through $C$ and meets $F G$ at $H$ . Find the area of the shaded region.

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Solution

The correct option is A $8$

Area of shaded part $=$ area of square - area of trapezoid
Area of square $= 4 \times 4 = 16$
Now, $△ A C D \sim △ A G H, ∴ \frac{A D}{A G} = \frac{C D}{H G} \Rightarrow H G = \frac{A G \times C D}{A D} = \frac{6 \times 1}{2} = 3$
Now, area of trapezoid $= \frac{1}{2} (C D + H G) \times D G = \frac{1}{2} \times (1 + 3) \times 4 = 8$
Required area $= 16 - 8 = 8$

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DEFG is a square and ABCD is a rectangle. A straight line is drawn from A passes through C and meets FG at H. Find the area of the shaded region.

The correct option is A 8Area of shaded part = area of square - area of trapezoidArea of square =4×4=16Now, △ACD∼△AGH,∴ADAG=CDHG⇒HG=AG×CDAD=6×12=3Now, area of trapezoid =12(CD+HG)×DG=12×(1+3)×4=8Required area =16−8=8

$D E F G$ is a square and $A B C D$ is a rectangle. A straight line is drawn from $A$ passes through $C$ and meets $F G$ at $H$ . Find the area of the shaded region.