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Question

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

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Solution

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

Equation of AB is given by

y1=6164(x4) or y=52x9

Equation of BC is given by

y6=4686(x6) or y=x+12

Equation of AC is given by

y1=4184(x4) or y=34x2

Area of ABC = area of trap. DABE + area of trap. EBCF - area of trap. DACF

= 64(52x9)dx+86(x+12)dx84(34x2)dx

=52[x22]649[x]64[x22]86+12[x]8634[x22]84+2[x]84

=54(3616)9(64)12(6436)+12(86)38(6416)+2(84)

=54×2018282+2438×48+8

=251814+2418+8=7 sq units


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