Question

Which of the following is the area of the red region in sq units?
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Answer 1

Answer:

9 sq. units

Step-by-step explanation:

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Answer 2

• The area of the red region si equal to (3/8)•LB unit² .

To Find :- The area of the red region in sq units ?

Solution :-

Assume length of bigger rectangle is L units and breadth is equal to B units .

As we can see that, Breadth is divided into 4 smaller rectangles and length is divided into 6 smaller rectangles .

So,

→ Length of each smaller rectangle = (L/6) units

→ Breadth of each smaller rectangle = (B/4) units

Now use shifting method and put smaller red rectangles in place of smaller blue rectangles . { Refer to image and shift them according to arrow sign . }

then,

→ Area of column { Along length } = L × (B/4) = (LB/4) units²

→ Area of row { Along breadth } = (L/6) × (3B/4) = (LB/8) { since first smaller rectangle area has already taken in column } units²

therefore,

→ Total area of red region = (LB/4) + (LB/8)

→ Total area of red region = (2LB + LB)/8

→ Total area of red region = (3/8)•LB units² .

Verification :-

Let Length = 6 units, Breadth = 4 units and each smaller rectangles are in the shape of a square of side 1 unit .

So,

→ Total red regions area = 9 square area

→ (3/8)•LB = 9 × (1)²

→ (3/8) × (6 × 4) = 9 × 1

→ (3/8) × 24 = 9 units²

→ 9 units² = 9 units²

→ LHS = RHS

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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