Question posted by Inz from Jakarta:
Question solved by Model Method:
The figure below consists of a square and a rectangle.
The ratio of the shaded area to the area of the square is 2:9.
The ratio of the shaded area to the area of the rectanlge is 1:6.
(A) Find the ratio of the area of the shaded part to the area of the total figure.
(B) If the area of the shaded part is 32 square cm, find the length of the square.
Step 1: This question involves the Overlapping Concept. We first draw 9 boxes to represent the area of the square and shade 2 boxes to represent the shaded part of the square.
Step 2: Next, we draw another box below equal to the size of the 2 shaded boxes to represent the area of the shaded part of the rectangle. This is 1/6 of the area of the rectangle.
Step 3: Then, we draw another 5 big boxes identical to this one to represent the remaining area of the rectangle. This is 5/6 of the area of the rectangle.
Step 4: Now, we sub-divide each of the 6 big boxes into 2 equal small boxes so that all the unknown parts will be equal. We then label the 2 shaded units as 32 (as given in the question).
From the model,
The ratio of the area of the shaded part to the area of the total figure is 2:19.
(No working needed as answer extracted directly from model. Note that in this case, the model is the working and the pupil will be accorded working marks based on the model drawn)
2 units ----------> 32
1 unit ----------> 32 / 2 = 16
9 units ----------> 9 x 16 = 144
144 = 12 x 12
Therefore, the length of the square is 12 square cm.
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