Question

The area of the
triangular region, in the following
figure, bounded by the lines 2x-y=1

and x+2y=13 and
Y-axis is​

Answer 1

Step-by-step explanation:

Given:Figure

To find: Area of triangle ADC.

Solution:

Tip:

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

2) Area of ∆ADC=$\bf \frac{1}{2} \times base \times height$

Method 1: Put the points into the formula

A(3,5), D(0,6.5) and C(0,-1)

$Ar(∆ADC)= \frac{1}{2} \left |3(6.5 -(-1)) + 0( - 1 - 5) + 0(5 -6.5)\right |$

$Ar(∆ADC)= \frac{1}{2} \left |3(7.5) \right |$

$Ar(∆ADC)= \frac{1}{2} \left |22.5\right |$

$\bf \red{Ar(∆ADC)= 11.25}$sq-units

Method 2: Find base and height of triangle.

It is clear from the figure that

Base(DC)=7.5 units

Height(BA)=3 units

Area of ∆ADC=$\frac{1}{2} \times base \times height$

Area of ∆ADC=$\frac{1}{2} \times 7.5 \times 3$

Area of ∆ADC=$\bf \green{11.25\:sq-units}$

Final answer:

The area of the triangular region, in the following figure, bounded by the lines

$2x-y=1$ and $x+2y=13$

and Y-axis is 11.25 sq-units.

Hope it helps you.

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