Question

find the areas of a triangle ABC whose vertices are a - 5 - 1 b 3,5 and c5,2​

Answer 1

Answer:

Area of triangle is 18 cm ^2.

Answer 2

The area of triange is 18 square units.

Step-by-step explanation:

The given three points A(- 5, - 1), B(3 , 5) and C(5, 2) ​ are vertices of triangle ABC.

To find, the area of triangle ABC = ?

We know that,

The area of triangle.

$=\dfrac{1}{2} [x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

$=\dfrac{1}{2} [(-5)(5-2)+3(2+1)+5(-1-5)]$

$=\dfrac{1}{2} [(-5)(3)+3(3)+5(-6)]$

$=\dfrac{1}{2} [-15+9-30]$

$=\dfrac{1}{2} [-45+9]$

$=\dfrac{1}{2} [-36]$ square units

= - 18 square units [ ∵ Area never be negative]

= 18 square units

Thus, the area of triange is 18 square units.