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# The angles between the diagonals of a rectangle is 30 degrees and each diagonal is 12 cm long. Find the area of the rectangle.

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The angles between the diagonals of a rectangle is 30 degrees and each diagonal is 12 cm long. Find the area of the rectangle.

Guest Dec 29, 2014

#1
+17746
+10

Draw a picture of this rectangle with its diagonals.

This picture contains four triangles. You know that two sides of each of these interior triangles are each 6 cm long. In two of the triangles, the angle contained between these sides is 30° and in the other two triangles, the angle is 150°.

One formula for the area of a triangle is:  Area  =  ½ · a · b · sin(C)  Where  a  and  b  are the lengths of the two sides that contain  ∠C.

So the area of two of the triangles is each:               Area  =  ½ · 6 · 6 · sin(30°)

while the area of each of the other two triangles is:   Area  =  ½ · 6 · 6 · sin(150°)

Add these four triangular areas to get the area of the rectangle.

geno3141  Dec 29, 2014
#1
+17746
+10

Draw a picture of this rectangle with its diagonals.

This picture contains four triangles. You know that two sides of each of these interior triangles are each 6 cm long. In two of the triangles, the angle contained between these sides is 30° and in the other two triangles, the angle is 150°.

One formula for the area of a triangle is:  Area  =  ½ · a · b · sin(C)  Where  a  and  b  are the lengths of the two sides that contain  ∠C.

So the area of two of the triangles is each:               Area  =  ½ · 6 · 6 · sin(30°)

while the area of each of the other two triangles is:   Area  =  ½ · 6 · 6 · sin(150°)

Add these four triangular areas to get the area of the rectangle.

geno3141  Dec 29, 2014
#2
+93025
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Geno....thanks for all those great answers to those geometry questions...!!!

CPhill  Dec 29, 2014
#3
+94202
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Yes, thank you Geno

Melody  Dec 30, 2014