Question

The area of the rectangle ABCD is 2 and BD=DE. Find the area of the shaded region.

Ans: 1
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Answer 1

Answer:

may be the answer of this question is 1

Answer 2

Given :-

• The area of the rectangle ABCD is 2 and BD = DE.
• AB = 1 .

To Find :-

• The area of the shaded region. ?

Answer :- (from image see construction) .

∆DFE ~ ∆BGE

so,

→ ED / DF = EB / BG

→ √5 / x = 2√5/(BC + CG)

→ √5/x = 2√5/(2 + x)

→ 2x = 2 + x

→ x = 2 .

then, in right angled ∆DFE,

→ EF = √{(√5)² - 2²)}

→ EF = √(5 - 4)

→ EF = 1 .

therefore,

→ Shaded region area = Area ∆AFE - Area ∆DFE

→ Shaded region area = {(1/2) * AF * EF} - {(1/2) * DF * EF}

→ Shaded region area = (1/2) * EF * (AF - DF)

→ Shaded region area = (1/2) * EF * AD

→ Shaded region area = (1/2) * 1 * 2

→ Shaded region area = 1 (d) (Ans.)

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