Question

What is the area of triangle RST?

Answer 1

Answer:  The required area of triangle RST is 9 sq. units.

Step-by-step explanation: We are given to find the area of triangle RST shown in the figure.

We know that the AREA of a triangle with base 'b' units and height 'h' units is given by

$A=\dfrac{1}{2}\times b\times h.$

From the figure, we note that in ΔRST,

base, b = RS = 6 units

and

height, h = UT = 3 units.

Therefore, the area of ΔRST,  will be

$A-{RST}=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 6\times 3=9~\textup{sq. units}.$

thus, the required area of triangle RST is 9 sq. units.

Answer 2

Answer-

$\boxed{\boxed{\text{Area}_{RTS}=9\ unit^2}}$

Solution-

We know that,

$\text{Area}=\dfrac{1}{2}\times\text{Base}\times \text{Height}$

From the diagram,

RS is the base and UT is the height of the triangle.

Applying distance formula,

$RS=\sqrt{(3+3)^2+(2-2)^2}=\sqrt{(6)^2}=6$

$UT=\sqrt{(-1+1)^2+(2+1)^2}=\sqrt{(3)^2}=3$

Putting the values,

$\text{Area}_{RTS}=\dfrac{1}{2}\times6\times3=9\ unit^2$