Question

Find the area of the triangle formed by the vertices (2, 3), (5, 6) and (7, 4)

Answer 1

Answer:

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Answer 2

Area of the given triangle is 6 sq unit.

Step-by-step explanation:

If, (x1, x2), (x2, y2) and (x3, y3) are the coordinates of vertices of triangle then

$Area =\frac{1}{2}(x_{1} (y_{2} -y_{3})+x_{2} (y_{3} -y_{1})+x_{3} (y_{1} -y_{2}))$

We have:

(x1, x2)=(2,3)

(x2, y2) =(5,6)

(x3, y3)=(7,4)

Substitute the known values and simplify.

$Area =\frac{1}{2}(x_{1} (y_{2} -y_{3})+x_{2} (y_{3} -y_{1})+x_{3} (y_{1} -y_{2}))\\\\\Rightarrow Area = \frac{1}{2}(2(6-4)+5(4-3)+7(3-6))\\ \\\Rightarrow Area = \frac{1}{2}(2\times 2+5\times 1+7\times (-3))\\\\\Rightarrow Area=\frac{1}{2}(4+5-21)\\\\ \Rightarrow Area=\frac{1}{2}(-12)\\\\ \Rightarrow Area=-6$

Since the Area of the triangle cannot be -ve, we will consider the numerical value only.

So Area of the given triangle is 6 sq unit.

Learn More:

The area of an isosceles traingle is 300cm2. The height of the traingle is 15 cm. Find the perimeter of the traingle.

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