Find Area of Shaded region (Page 193)

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Find Area of Shaded region (Page 193) In each of the figures given below, find the fraction of the big square that the shaded region occupies Let’s do it one by one Figure 1 Now, Area of Blue triangle = 1/2 × Area of square If we divide divide blue triangle into 4 parts Shaded region is ¼ of blue triangle (top left) ¼ of blue triangle (bottom right) ½ × ¼ of blue triangle (Middle half) Thus, Area of shaded region = (𝟏/𝟒+𝟏/𝟒+𝟏/𝟐 ×𝟏/𝟒) × Area of blue triangle = (1/4+1/4+1/(2 × 4)) × Area of blue triangle = ((1 + 1)/4+1/8) × Area of blue triangle = (2/4+1/8) × Area of blue triangle = (4/8+1/8) × Area of blue triangle = ((4 + 1)/8) × Area of blue triangle = 𝟓/𝟖 × Area of blue triangle = 5/8 × 1/2 × Area of square = 𝟓/𝟏𝟔 × Area of square Figure 2 Now, Area of Blue square = 1/4 × Area of square If we divide divide blue square into 8 parts Shaded region is 2 × 1/8 of blue sqauare Thus, Area of shaded region = 2 ×1/8 × Area of blue square = 𝟏/𝟒 × Area of blue square = 1/4 × 1/4 × Area of square = 𝟏/𝟏𝟔 × Area of square