ConceptArea of a Triangle

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#### Question

If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.

#### Solution

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Find the values of k so that the area of the triangle with vertices (k + 1, 1), (4, -3) and (7, -k) is 6 sq. units.

If P(–5, –3), Q(–4, –6), R(2, –3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area.

If the points P(–3, 9), Q(*a, b*) and R(4, – 5) are collinear and *a + b *= 1, find the values of *a* and* b*.

In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, −1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) respectively. If F is the mid-point of BC, find the areas of ∆ABC and ∆DEF.

Find the area of the triangle whose vertices are:

(8, 1), (k, -4), (2, -5)

#### Reference Material

Solution for concept: Area of a Triangle. For the course 8th-10th CBSE