Q. 135.0( 1 Vote )

# Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3). **[CBSE 2014]**

**[CBSE 2014]**

Answer :

It is given that the vertices are A (2, 0), B (4, 5) and C (6, 3).

Now,

Equation of line segment AB is

⇒

=> y – 0 = 5x - 10

Equation of line segment BC is

⇒

=> 2y – 10 = -2x + 8

=> 2y = -2x + 18

=> y = -x + 9 …(2)

Equation of line segment CA is

⇒

=> -4y + 12 = -3x + 18

=> 4y = 3x - 6

…(3)

Thus,

Area(ΔABC) = Area ABLA + Area BLMCA – Area ACMA

⇒

⇒

⇒

⇒

= 13 – 6

= 7 units.

Rate this question :

Draw a rough sketch of the given curve y = 1 + |x +1|, x = –3, x = 3, y = 0 and find the area of the region bounded by them, using integration.

Mathematics - ExemplarCompute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.

Mathematics - ExemplarUsing integration find the area of the region

}

Mathematics - Board PapersFind the area of the region {(x, y) : x^{2} + y^{2}≤ 4, x + y ≥ 2}.

Find the area of region bounded by the triangle whose vertices are (–1, 1), (0, 5) and (3, 2), using integration.

Mathematics - ExemplarEvaluate as limit of sums.

**OR**

Using integration, find the area of the following region:

Mathematics - Board Papers

The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ is.

Mathematics - ExemplarFind the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.

Mathematics - Exemplar