Can someone please help?

Find the perimeter of rhombus star

Degger [83]

Answer:

$4\sqrt{10}$

Step-by-step explanation:

Perimeter of the rhombus, STAR, is the sum of the length of all it's 4 sides.

The coordinates of its vertices are given as,

S(-1, 2)

T(2, 3)

A(3, 0)

R(0, -1)

Length of each side can be calculated using the distance formula given as $d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}$

Find the length of each side ST, TA, AR, RS, using the above formula by plugging in the coordinate values (x, y) of each vertices.

$ST = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

S(-1, 2) => (x1, y1)

T(2, 3) => (x2, y2)

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

$ST = \sqrt{(3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10}$

$TA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

T(2, 3) => (x1, y1)

A(3, 0) => (x2, y2)

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

$TA = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}$

$AR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

A(3, 0) => (x1, y1)

R(0, -1) => (x2, y2)

$AR = \sqrt{(0 - 3)^2 + (-1 - 0)^2}$

$AR = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$

$RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

R(0, -1) => (x1, y1)

S(-1, 2) => (x2, y2)

$RS = \sqrt{(-1 - 0)^2 + (2 -(-1))^2}$

$RS = \sqrt{(-1)^2 + (3)^2} = \sqrt{1 + 9} = \sqrt{10}$

$Perimeter = ST + TA + AR + RS$

$Perimeter = \sqrt{10} + \sqrt{10} + \sqrt{10} + \sqrt{10} = 4\sqrt{10}$

4 0

4 years ago

What is this -5g-13g=54?

-BARSIC- [3]

The answer is -3. Now I just got 100 points!!!

4 0

3 years ago

Read 2 more answers

The table below lists the masses and volumes of several pieces of the same type of metal. There is a proportional relationship b

Murrr4er [49]

Given the table below which lists the masses and volumes of several pieces of the same type of metal.

From the table the ratio of the mass to the volume of the metal of mass 34.932 is 34.932 / 4.1 = 8.52
the ratio of the mass to the volume of the metal of mass 47.712 is 47.712 / 5.6 = 8.52
the ratio of the mass to the volume of the metal of mass 61.344 is 61.344 / 7.2 = 8.52
the ratio of the mass to the volume of the metal of mass 99.684 is 99.684 / 11.7 = 8.52

MASS (grams) VOLUME (cubic cm.)
34.932 4.1
47.712 5.6
61.344 7.2
99.684 11.7

Since the ratio of the various masses to the volume of the metals is the same, so there is a relationship between the mass and the volume of the piece of metal.

If the volume of a piece of metal is 15.3 cubic cm, then the mass of the metal is given by 15.3 * 8.52 = 130.356 grams.

3 0

4 years ago

What is the area of a trapezoid that has bases measuring 19 centimeters and 23

Afina-wow [57]

Answer: 294

Step-by-step explanation:

sum of bases:

42

multiply by height:

588

divide by 2:

294

5 0

3 years ago

Can someone PLEASE HELP ME! Choose the correct answer, if your correct ill mark u as the best choice!

horrorfan [7]

Answer:

number 2

Step-by-step explanation:

8 0

3 years ago