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

Answer:

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

RS=$\sqrt{(3+3)^2+(0)^2}$

Simplify: we get

RS=$\sqrt{36} =6$ unit.

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

then:

TU=$\sqrt{(-1-(-1))^2+(2-(-1))^2}$ or

TU=$\sqrt{(-1+1)^2+(2+1)^2}$ or

Simplify:

$TU=\sqrt{0+9} =\sqrt{9} =3$ 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 = $\frac{b\cdot h}{2}$ 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 $\triangle RST$ = $\frac{RS \cdot TU}{2}$

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

Area of $\triangle RST$ = $\frac{6\cdot3}{2}$

Simplify:

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