Question

Alice drew two game boards. These game boards are the same shape and the same size. She said that

1/2
of each game board is shaded.
Is Alice correct or incorrect? Choose the text to complete the statement.
Alice is _________ because _____________________________________________________.

(do not delete this question nor reporting this question)

Answer 1

Alice is correct because area of shaded region of both the gameboards are equal.

Explanation:

Here it is given that both the gameboards are of same shape and size and Alice stated that the area of shaded regions of both the gameboards are same.

Let us take the length of the board be "l" and its breadth be "b" .

Initial area of the gameboard will be lb since it is a rectangle.

1st case :-

breadth of the shaded region= b

length of the shaded region = l/2 (since the length becomes half )

Area of the shaded region = b*l/2 = lb/2 .

2nd case :-

breadth of the shaded region = b/2 ( since breadth becomes half. )

length of the shaded region = l

Area of the shaded region = l/2

Area of the shaded region = b/2*l = lb/2 .

As we can see that the area of shaded region in both shaded region in both cases are equal also it is half of the total area of the rectangle. Hence Alice was correct.

Hence the area of the shaded regions in both the cases are similar and half of board in case is shaded .