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Step2247 [10]
3 years ago
7

The sides of a rhombus with angle of 60° are 6 inches. Find the area of the rhombus.

Mathematics
1 answer:
ehidna [41]3 years ago
6 0
1. Check the drawing of the rhombus ABCD in the picture attached.

2. m(CDA)=60°, and AC and BD be the diagonals and let their intersection point be O.

3. The diagonals:
     i) bisect the angles so m(ODC)=60°/2=30°

     ii) are perpendicular to each other, so m(DOC)=90°

4. In a right triangle, the length of the side opposite to the 30° angle is half of the hypothenuse, so OC=3 in.

5. By the pythagorean theorem, DO= \sqrt{ DC^{2}- OC^{2} }=  \sqrt{ 6^{2}- 3^{2} }=\sqrt{ 36- 9 }=\sqrt{ 27 }= \sqrt{9*3}= 
=\sqrt{9}* \sqrt{3} =3\sqrt{3}  (in)

6. The 4 triangles formed by the diagonal are congruent, so the area of the rhombus ABCD = 4 Area (triangle DOC)=4*\frac{DO*OC}{2}=4 \frac{3 \sqrt{3} *3}{2}==2*9 \sqrt{3}=18 \sqrt{3} (in^{2})

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Im assuming youre trying to answer what is the 60% height, it would be 3ft

Step-by-step explanation:


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The maximum number of marks attainable at a mathematics competition is 60. Kate obtains 40 marks, Priya obtains 46 marks, and No
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A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90 degrees.What depth will provid
fredd [130]

Answer:

18 in^2

Step-by-step explanation:

<em>1  )The three sides of the gutter add up to 12</em>

            2x+ y = 12  

<em>2)  Subtract 2x from both sides. </em>

           y = 12 — 2x  

<em>3 )Find the area of the rectangle in terms of x and simplify.</em>

    Area = xy = x(12 — 2x) = -2x^2+12x = f(x)  

<em>4 )  x=-b/2a</em>

     <em>x co-ordinate of the vertex= -12/2(-2)=3</em>

<em>5 )Plug in 3 for x into they equation.</em>

    y co-ordinate of the vertex= 12 — 2(3) = 6  

<em>6  )  Plug in 3 for x and 6 for y.  </em>

      Area= xy = 3(6) = 18  

RESULT  

            18 in^2

 

 

 

 

7 0
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