Question

Find the area of the triangle with vertices A(5, 0), B(8, 0) and C(8, 4).​

Answer 1

Answer:

Area of the triangle= 1/2× b× h

=1/2 × 3×4

=6 units.

I wrote base as 3 and height as 4 because if you mark the vertices on a graph and join the vertices you'll get the base and height.

Answer 2

Answer :

Area = 6 square units

Step-by-step explanation :

METHOD - 1 :

  ⇒ Plotting points :

        When we plot the points A(5,0), B(8,0) and C(8,4) , we get a right angled triangle.  [ refer to the attachment ]

   base = 8 - 5 = 3 units

   height = 4 - 0 = 4 units

we know,

   Area of right angled triangle =  $\bf \frac{1}{2} \times base \times height$

                 

                      $Area =\frac{1}{2} \times 3 \times 4 \\\\ Area = \frac{1}{\not 2} \times 3 \times \not{4} 2 \\\\ Area = 2\times 3\\\\ \text{Area = 6 square units}$

METHOD - 2 :

  ⇒ Using formula :

    Let

• A(5,0) = (x₁ , y₁)
• B(8,0) = (x₂ , y₂)
• C(8,4) = (x₃ , y₃)

$\bf Area \ of \ the \ triangle =\frac{1}{2} |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

                                    $=\frac{1}{2} |5(0-4)+8(4-0)+8(0-0)| \\\\ =\frac{1}{2} |5(-4)+8(4)+8(0)| \\\\ =\frac{1}{2} |-20+32+0| \\\\ =\frac{1}{2} |12| \\\\ \bf =6 \ square \ units$

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