 ## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 33 of Exercise 21.3

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33
##### Using integration, find the area of the triangle ABC coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4).

To find area of ΔABC with A (4,1), B(6,6) and C(8,4)

Equation of AB,    ...(i)

Equation of BC, y – 6 = – 1(x – 6)

y = – x + 12 ...(ii)

Equation of AC, These are shown in the graph below: - Clearly, Area of ΔABC = Area ADB + Area BDC   Similarly,       Thus, Area ABC = Area ADB + Area BDC

= = 64 – 56

= 7 sq. units

The area of the triangle ABC coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4) is 7 sq. Units

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