Question

Find the area of triangle formed by the vertices (−3,0),(−3, −4) and (4,0).​

Answer 1

Answer:

Area of the triangle = 14.

Step-by-step explanation:

Given:

The vertices of triangle: (-3, 0), (-3, -4) and (4,0).

To Find:

The area of the triangle.

Solution:

We know that,

Area of triangle = 1/2 [x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)]

Where,

x₁ = -3

x₂ = -3

x₃ = 4

y₁ = 0

y₂ = -4

y₃ = 0

Now, substitute the values in the formula.

=> 1/2 [(-3)(-4-0)+(-3)(0-0)+(4)(0-(-4))]

=> 1/2 [(-3)(-4)+(-3)(0)+(4)(4)]

=> 1/2 [(12)+0+(16)]

=> 1/2 (12+016)

=> 1/2 (28)

=> 14

So, the area of the triangle is 14.

Answer 2

Answer:

Given :-

• A triangle formed by the vertices (- 3 , 0) , (- 3 , - 4) and (4 , 0).

To Find :-

• What is the area of triangle.

Formula Used :-

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\bigg]}}}$

Solution :-

Given points :

$\mapsto \bf A(- 3 , 0)$

$\mapsto \bf B(- 3 , - 4)$

$\mapsto \bf C(4 , 0)$

Here,

❒ $\sf x_1 =\: - 3$

❒ $\sf y_1 =\: 0$

❒ $\sf x_2 =\: - 3$

❒ $\sf y_2 =\: - 4$

❒ $\sf x_3 =\: 4$

❒ $\sf y_3 =\: 0$

According to the question by using the formula we get,

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[(- 3)\{(- 4) - (0)\} + (- 3)\{(0) - (0)\} + (4)\{(0) - (4)\}\bigg]$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[(- 3)(- 4) + (- 3)(0) + (4)(- 4)\bigg]$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[12 + 0 + (- 16)\bigg]$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[12 - 16\bigg]$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{1}{2}\bigg[- 4\bigg]$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{- \cancel{4}}{\cancel{2}}$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \dfrac{- 2}{2}$

$\small\longrightarrow \sf Area_{(Triangle)} =\: - 2\: \: \bigg\lgroup \sf\bold{\purple{Area\: can't\: be\: negetive\: (- ve)}}\bigg\rgroup$

$\small\longrightarrow \sf\bold{\red{Area_{(Triangle)} =\: 2\: square\: units}}$

${\small{\bold{\underline{\therefore\: The\: area\: of\: triangle\: is\: 2\: square\: units\: .}}}}$