Question 4 - Figure it out - Page 160 - Chapter 7 Class 8 - Area (Ganita Prakash II)

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Question 4 What fraction of the total area of the rectangle is the area of the blue region?We label the rectangle and the Triangle Let Length of Rectangle = l Breadth of Rectangle = b Thus, AB = CD = l AD = BC = b For Triangles ∆ APB & ∆ CPD Let’s draw Height from vertex P Now, finding Area of Triangle Area ∆ APB Here, Height = PQ Base = AB = l So, Area ∆ APB = 1/2 × Base × Height = 1/2 × PQ × AB = 𝟏/𝟐 × PQ × l Area ∆ CPD Here, Height = PR Base = CD = l So, Area ∆ CPD = 1/2 × Base × Height = 1/2 × PR × CD = 𝟏/𝟐 × PR × l Now, Area of Blue Region = Area ∆ APB + Area ∆ CPD = 𝟏/𝟐 × PQ × l + 𝟏/𝟐 × PR × l = 1/2 × l × (PQ + PR) Since PQ + PR = b = 1/2 × l × b Since Area of Rectangle ABCD = l × b = 𝟏/𝟐 × Area of Rectangle ABCD Thus, Blue Region is half of the Area of Rectangle