Question

What is the area (sq units) of the shaded region if the square
ABCD is divided into 9 equal square each having length of 1 unit and DE = 1/3 DA?

1. 2
2. 3
3. 4
4. 6


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Answer 1

Answer:

4

Step-by-step explanation:

Answer 2

The required area is 3 sq units. (Option 2)

Given:

DE=1/3 DA

To find:

The area of the shaded region

Solution:

We know that ABCD is divided into 9 equal squares.

So, each side will be divided into three equal parts.

Each of these squares has a length equal to 1 unit.

1/3 of AB=1/3 of BC=1/3 of CD=1/3 DA=1 unit

We know that DE=1/3 of DA.

So, DE=1 unit.

AB=BC=CD=DA=3 units

AE=DA-DE=3-1=2 units

The required area of the  ΔACE=1/2×base×height

=1/2×AE×AB

=1/2×2×3

=3 sq units

Therefore, the required area is 3 sq units.

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