Area of the triangle formed by the points `((a+3)(a+4),\ a+3),\ ((a+2)(a+3),(a+2))a n d\ (a+1),\ (a+2),\ (a+1)` is `25 a^2` b. `5^2` c. `24 a^2` d. none of these

Explanation

The given points are (a + 3) (a + 4), a + 3, (a + 2) (a + 3), (a + 2) and (a + 1) (a + 2), (a + 1).

Let A be the area of the triangle formed by these points.

Then A=`1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

A=`1/2[(a+3)(a+4)(a+2-a-1)-(a+2)(a+3)(a+1-a-3)+(a+1)(a+2)(a+3-a-2)]`

A=`1/2(a^2+7a-12-2a^2-10a-12+a^2+3a+2]`

A=`1`