Exercise 5.1: Area of a Triangle and Quadrilateral

Exercise 5.1

1. Find the area of the triangle formed by the points

(i) (1,–1), (–4, 6) and (–3, –5) 

(ii) (–10, –4), (–8, –1) and (–3, –5)

2. Determine whether the sets of points are collinear?

(i) (-1/2, 3) , (–5, 6) and (–8, 8) (ii) (a, b+c), (b, c+a) and (c, a+b)

3. Vertices of given triangles are taken in order and their areas are provided aside. In each case, find the value of ‘p ’

4. In each of the following, find the value of ‘a’ for which the given points are collinear.

(i) (2, 3), (4, a) and (6, –3) (ii) (a, 2–2a), (–a+1, 2a) and (–4–a, 6–2a)

5. Find the area of the quadrilateral whose vertices are at

(i) (–9, –2), (–8, –4), (2, 2) and (1, –3) (ii) (–9, 0), (–8, 6), (–1, –2) and (–6, –3)

6. Find the value of k, if the area of a quadrilateral is 28 sq.units, whose vertices are (–4, –2), (–3, k), (3, –2) and (2, 3)

7. If the points A(-3, 9) , B (a,b) and C(4, - 5) are collinear and if a + b = 1 , then find a and b.

8. Let P(11, 7) , Q(13.5, 4) and R(9.5, 4) be the mid-points of the sides AB, BC and AC respectively of ΔABC . Find the coordinates of the verticesA, B and C. Hence find the area of ΔABC and compare this with area of ΔPQR.

9. In the figure, the quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio.

10. A triangular shaped glass with vertices at A(- 5, - 4) , B(1, 6) and C(7, - 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied.

11. In the figure, find the area of (i) triangle AGF  (ii) triangle FED (iii) quadrilateral BCEG

Answers:

1.(i) 24 sq. units 

(ii) 11.5 sq. units 

2.(i) collinear 

(ii) collinear

3.(i) 44 (ii) 13

4.(i) 0 (ii) 1/2 or -1

5.(i) 35 sq.units (ii) 34 sq.units

6. -5

7. 2,-18.24 sq. units, area(∆ABC) = 4 × area(∆PQR)

9. 38 sq.units

10. 10 cans

11.(i) 3.75 sq. units (ii) 3 sq. units (iii) 13.88 sq. units