Question

The students of class X of a school undertake to work for the campaign “Say no to
plastic' in a city. They took the map of the city and form coordinate plane on it to
divide their areas. Group A took the region covered between the coordinates (1, 1),
(-3, 2), (-2,-2) and (1, -3) taken in order. Find the area of the region covered by
group A.​

Answer 1

13.5 sq. units.

Step-by-step explanation:

Let the region is a quadrilateral ABCD with vertices A(1,1), B(-3,2), C(-2,-2), and D(1,-3).

Now, the area of the triangle Δ ABC = $\frac{1}{2}|1(2 + 2) - 3(- 2 - 1) - 2(1 - 2)| = 7.5$ sq. units.

Again, the area of the triangle Δ ACD = $\frac{1}{2}|1(- 2 + 3) - 2(- 3 - 1) + 1(1 + 2)| = 6$ sq, units.

Therefore, the total area of the region ABCD = (7.5 + 6) = 13.5 sq. units. (Answer)