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  • Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 33 Maths.

Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 33 Maths.

Answers (1)

Answer:

7sq. Units.

Hint:

Use conceptual part.

Given:

Triangle ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C (8,4).

Solution:

Equation of AB is given by

y=-\frac{5}{2}x-9

                Equation of BC is given by

y=-x+12

Equation of AC is given by

y=\frac{3}{4}x-2

Area of  ABC

\begin{aligned} &=\int_{4}^{6}\left(y_{A B}-y_{A C}\right) d x+\int_{6}^{8}\left(y_{B C}-y_{A C}\right) d x \\ &=\int_{4}^{6}\left(\frac{5}{2} x-9-\frac{3}{4} x+2\right) d x+\int_{0}^{8}\left(-x+12-\frac{3}{4} x+2\right) d x \\ &=\int_{4}^{6}\left(\frac{7}{4} x-7\right) d x+\int_{6}^{8}\left(-\frac{7 x}{4}+14\right) d x \\ &=\left[\frac{7 x^{2}}{8}-7 x\right]_{4}^{6}+\left[-\frac{7 x^{2}}{8}+14 x\right]_{6}^{8} \\ &=\left[\left(\frac{63}{2}-42\right)-(14-28)\right]+\left[(-56+112)-\left(\frac{-63}{2}\right)+84\right] \\ &=\left[\frac{63}{2}-42-14+28-56+112+\frac{63}{2}-84\right] \\ &=63-56 \\ &=7 \text { sq.units } \end{aligned}

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