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=(1)/(2)* b* 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}=(1)/(2)* b* h=(1)/(2)* 6* 3=9~\textup{sq. units}.`

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

Answer 2

`\boxed{\boxed{\text{Area}_(RTS)=9\ unit^2}}`

Solution-

We know that,

`\text{Area}=(1)/(2)*\text{Base}* \text{Height}`

From the diagram,

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

Applying distance formula,

`RS=√((3+3)^2+(2-2)^2)=√((6)^2)=6`

`UT=√((-1+1)^2+(2+1)^2)=√((3)^2)=3`

Putting the values,

`\text{Area}_(RTS)=(1)/(2)*6*3=9\ unit^2`