Mathematics, 03.01.2020 00:31 lullexxxx

Find the area of a rhombus with side length 6 and an interior angle with measure $120^\circ$.

Answers: 3

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Answer from: Svetakotok

Area of Rhombus is 31.176 unit² (Approx.)

Given that;

Length of rhombus side = 6 unit

Angle = 120°

Find:

Area of Rhombus

Computation:

Area of Rhombus = Side²(Sin θ)

Area of Rhombus = 6²(Sin 120)

Area of Rhombus = 36(0.866)

Area of Rhombus = 31.176 unit² (Approx.)

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$Find the area of a rhombus with side length 6 and an interior angle with measure $120^\circ$.$

Answer from: Harini5721

The area of a rhombus is $18\sqrt{3}$ square units.

Step-by-step explanation:

Side length of rhombus = 6 units.

Interior angle of rhombus = 120°

another Interior angle of rhombus = 180°-120° = 60°.

Draw an altitude.

In a right angled triangle

$\sin \theta=\frac{opposite}{hypotenuse}$

$\sin (60)=\frac{h}{6}$

$\frac{\sqrt{3}}{2}=\frac{h}{6}$

Multiply both sides by 6.

$3\sqrt{3}=h$

The height of the rhombus is $3\sqrt{3}$ .

Area of a rhombus is

$Area=base\times height$

$Area=6\times 3\sqrt{3}$

$Area=18\sqrt{3}$

Therefore, the area of a rhombus is $18\sqrt{3}$ square units.

Answer from: Quest

it depends on the weather. because i have flown to seattle when it was pouring down rain and there was one time i flew to ohio when it was snowing hard. whats your situation.

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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Find the area of a rhombus with side length 6 and an interior angle with measure $120^\circ$....