Question

TIMED HELP PLEASE!!!!

What is the area of triangle RST?


____ square units

Answer 1

The base must be perpendicular to the height for area= bh/2.

We can use RS as the base and TU as the height.
6*3/2
18/2
9

Final answer: 9 units^2

Answer 2

The coordinate of triangle RST from the figure are;

R = (-3,2), S=(3,2) and T=(-1,-1). also the coordinate of U = (-1, 2).

Distance Formula: It is used to determine the distance between two points with the coordinates
`(x_(1),y_(1))` and
`(x_(2),y_(2))` i.e,

Distance =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Now, using above formula to find the sides of a given triangle:

Calculate the length of RS , where R=(-3,2) and S=(3,2);

RS=
`√((3-(-3))^2+(2-2)^2)` or

RS=
`√((3+3)^2+(0)^2)`

Simplify: we get

RS=
`√(36) =6` unit.

Similarly, for TU, where T=(-1.-1) and U=(-1,2).

then:

TU=
`√((-1-(-1))^2+(2-(-1))^2)` or

TU=
`√((-1+1)^2+(2+1)^2)` or

Simplify:

`TU=√(0+9) =√(9) =3` unit.

Since, we have to calculate the Area of triangle RST.

To, find the area of a triangle, multiply the base by the height and then divide it by 2.

i.e,

Area of triangle =
`(b\cdot h)/(2)` where b is the base and h is the height of the triangle.

Here, in the given triangle RST, the base of the triangle = RS and the height of the triangle= TU.

Area of
`\triangle RST` =
`(RS \cdot TU)/(2)`

Substitute the value of RS = 6 unit and TU= 3 unit in the above formula;

Area of
`\triangle RST` =
`(6\cdot3)/(2)`

Simplify:

Area of
`\triangle RST`=
`3\cdot 3=9` square unit.