Question

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

Answer 1

Answer:

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Answer 2

The area of the triangle ABC is 32 square units.

Step-by-step explanation:

Given,

The three vertices  of the triangle are A(- 5, - 1), B(3, - 5) and C( 5, 2).

To find, the area of the triangle ABC = ?

We know that.

The area of triangle

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

∴ The area of the triangle ABC

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

$=\dfrac{1}{2} [(-5)(-7)+3(3)+5(4)]$

$=\dfrac{1}{2} [35+9+20]$

$=\dfrac{1}{2} [64]$

= 32 square units

Thus, the area of the triangle ABC is 32 square units.